LMFDB - Embedded newform 546.2.bu.b.71.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(71,546)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 0, 5]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("546.71");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bu (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$14$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			71.10
Character	$\chi$	$=$	546.71
Dual form			546.2.bu.b.323.10

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 - 0.258819i) q^{2} +(-0.625096 - 1.61532i) q^{3} +(0.866025 - 0.500000i) q^{4} +(0.828570 + 0.828570i) q^{5} +(-1.02187 - 1.39849i) q^{6} +(0.258819 - 0.965926i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.21851 + 2.01946i) q^{9} +O(q^{10})$	\(q+(0.965926 - 0.258819i) q^{2} +(-0.625096 - 1.61532i) q^{3} +(0.866025 - 0.500000i) q^{4} +(0.828570 + 0.828570i) q^{5} +(-1.02187 - 1.39849i) q^{6} +(0.258819 - 0.965926i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.21851 + 2.01946i) q^{9} +(1.01479 + 0.585888i) q^{10} +(-1.25192 - 4.67223i) q^{11} +(-1.34901 - 1.08636i) q^{12} +(0.0707604 - 3.60486i) q^{13} -1.00000i q^{14} +(0.820469 - 1.85634i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.258842 - 0.448327i) q^{17} +(-1.62024 + 2.52484i) q^{18} +(5.50267 + 1.47444i) q^{19} +(1.13185 + 0.303278i) q^{20} +(-1.72206 + 0.185721i) q^{21} +(-2.41852 - 4.18900i) q^{22} +(-2.54064 + 4.40052i) q^{23} +(-1.58421 - 0.700193i) q^{24} -3.62694i q^{25} +(-0.864656 - 3.50034i) q^{26} +(4.64885 + 2.32125i) q^{27} +(-0.258819 - 0.965926i) q^{28} +(1.83703 + 1.06061i) q^{29} +(0.312056 - 2.00544i) q^{30} +(4.11077 - 4.11077i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-6.76456 + 4.94284i) q^{33} +(-0.366058 - 0.366058i) q^{34} +(1.01479 - 0.585888i) q^{35} +(-0.911557 + 2.85816i) q^{36} +(-9.86282 + 2.64273i) q^{37} +5.69678 q^{38} +(-5.86723 + 2.13908i) q^{39} +1.17178 q^{40} +(-6.46664 + 1.73273i) q^{41} +(-1.61532 + 0.625096i) q^{42} +(-0.253885 + 0.146580i) q^{43} +(-3.42031 - 3.42031i) q^{44} +(-3.51145 - 0.164928i) q^{45} +(-1.31513 + 4.90814i) q^{46} +(8.54481 - 8.54481i) q^{47} +(-1.71146 - 0.266310i) q^{48} +(-0.866025 - 0.500000i) q^{49} +(-0.938722 - 3.50336i) q^{50} +(-0.562390 + 0.698360i) q^{51} +(-1.74115 - 3.15728i) q^{52} +9.52725i q^{53} +(5.09123 + 1.03894i) q^{54} +(2.83396 - 4.90857i) q^{55} +(-0.500000 - 0.866025i) q^{56} +(-1.05801 - 9.81023i) q^{57} +(2.04895 + 0.549013i) q^{58} +(1.53749 + 0.411970i) q^{59} +(-0.217623 - 2.01787i) q^{60} +(5.90367 + 10.2255i) q^{61} +(2.90675 - 5.03464i) q^{62} +(1.37645 + 2.66559i) q^{63} -1.00000i q^{64} +(3.04551 - 2.92825i) q^{65} +(-5.25477 + 6.52521i) q^{66} +(2.99192 + 11.1660i) q^{67} +(-0.448327 - 0.258842i) q^{68} +(8.69639 + 1.35320i) q^{69} +(0.828570 - 0.828570i) q^{70} +(0.487312 - 1.81867i) q^{71} +(-0.140751 + 2.99670i) q^{72} +(4.68386 + 4.68386i) q^{73} +(-8.84276 + 5.10537i) q^{74} +(-5.85867 + 2.26719i) q^{75} +(5.50267 - 1.47444i) q^{76} -4.83704 q^{77} +(-5.11367 + 3.58474i) q^{78} +2.53289 q^{79} +(1.13185 - 0.303278i) q^{80} +(0.843575 - 8.96038i) q^{81} +(-5.79783 + 3.34738i) q^{82} +(11.7215 + 11.7215i) q^{83} +(-1.39849 + 1.02187i) q^{84} +(0.157002 - 0.585939i) q^{85} +(-0.207296 + 0.207296i) q^{86} +(0.564904 - 3.63038i) q^{87} +(-4.18900 - 2.41852i) q^{88} +(-0.717827 - 2.67897i) q^{89} +(-3.43449 + 0.749523i) q^{90} +(-3.46371 - 1.00135i) q^{91} +5.08128i q^{92} +(-9.20983 - 4.07058i) q^{93} +(6.04209 - 10.4652i) q^{94} +(3.33767 + 5.78102i) q^{95} +(-1.72206 + 0.185721i) q^{96} +(3.95229 + 1.05901i) q^{97} +(-0.965926 - 0.258819i) q^{98} +(12.2128 + 7.83718i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 8 q^{6} - 24 q^{9}+O(q^{10}) $ 56 * q + 8 * q^6 - 24 * q^9	$ 56 q + 8 q^{6} - 24 q^{9} + 24 q^{10} + 8 q^{11} + 24 q^{13} + 4 q^{15} + 28 q^{16} - 4 q^{17} - 8 q^{18} + 8 q^{19} + 4 q^{21} - 8 q^{23} - 8 q^{24} - 4 q^{26} - 24 q^{27} - 8 q^{30} - 8 q^{31} + 8 q^{33} - 24 q^{34} + 24 q^{35} - 12 q^{36} - 8 q^{37} - 20 q^{39} - 28 q^{41} + 8 q^{44} + 72 q^{45} - 20 q^{46} + 64 q^{50} + 16 q^{54} + 8 q^{55} - 28 q^{56} + 4 q^{58} - 8 q^{59} + 20 q^{60} + 8 q^{61} - 32 q^{62} - 16 q^{63} - 24 q^{65} + 32 q^{66} - 16 q^{69} - 112 q^{71} + 8 q^{73} + 48 q^{74} + 40 q^{75} + 8 q^{76} + 16 q^{79} + 12 q^{81} - 4 q^{83} - 4 q^{84} + 32 q^{85} - 16 q^{86} - 144 q^{87} + 88 q^{89} - 8 q^{90} - 8 q^{91} + 52 q^{93} - 8 q^{94} - 48 q^{95} + 4 q^{96} - 64 q^{97} + 56 q^{99}+O(q^{100}) $ 56 * q + 8 * q^6 - 24 * q^9 + 24 * q^10 + 8 * q^11 + 24 * q^13 + 4 * q^15 + 28 * q^16 - 4 * q^17 - 8 * q^18 + 8 * q^19 + 4 * q^21 - 8 * q^23 - 8 * q^24 - 4 * q^26 - 24 * q^27 - 8 * q^30 - 8 * q^31 + 8 * q^33 - 24 * q^34 + 24 * q^35 - 12 * q^36 - 8 * q^37 - 20 * q^39 - 28 * q^41 + 8 * q^44 + 72 * q^45 - 20 * q^46 + 64 * q^50 + 16 * q^54 + 8 * q^55 - 28 * q^56 + 4 * q^58 - 8 * q^59 + 20 * q^60 + 8 * q^61 - 32 * q^62 - 16 * q^63 - 24 * q^65 + 32 * q^66 - 16 * q^69 - 112 * q^71 + 8 * q^73 + 48 * q^74 + 40 * q^75 + 8 * q^76 + 16 * q^79 + 12 * q^81 - 4 * q^83 - 4 * q^84 + 32 * q^85 - 16 * q^86 - 144 * q^87 + 88 * q^89 - 8 * q^90 - 8 * q^91 + 52 * q^93 - 8 * q^94 - 48 * q^95 + 4 * q^96 - 64 * q^97 + 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{12}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$2$	0.965926	−	0.258819i	0.683013	−	0.183013i
$3$	−0.625096	−	1.61532i	−0.360899	−	0.932605i
$3$	−0.625096	−	1.61532i	−0.360899	−	0.932605i
$4$	0.866025	−	0.500000i	0.433013	−	0.250000i
$5$	0.828570	+	0.828570i	0.370548	+	0.370548i	0.867677	−	0.497129i	$-0.165612\pi$
$5$	0.828570	+	0.828570i	0.370548	+	0.370548i	−0.497129	+	0.867677i	$0.665612\pi$
$6$	−1.02187	−	1.39849i	−0.417177	−	0.570932i
$7$	0.258819	−	0.965926i	0.0978244	−	0.365086i
$7$	0.258819	−	0.965926i	0.0978244	−	0.365086i
$8$	0.707107	−	0.707107i	0.250000	−	0.250000i
$9$	−2.21851	+	2.01946i	−0.739503	+	0.673153i
$10$	1.01479	+	0.585888i	0.320904	+	0.185274i
$11$	−1.25192	−	4.67223i	−0.377468	−	1.40873i	−0.849705	−	0.527258i	$-0.823220\pi$
$11$	−1.25192	−	4.67223i	−0.377468	−	1.40873i	0.472238	−	0.881471i	$-0.343446\pi$
$12$	−1.34901	−	1.08636i	−0.389425	−	0.313605i
$13$	0.0707604	−	3.60486i	0.0196254	−	0.999807i
$13$	0.0707604	−	3.60486i	0.0196254	−	0.999807i
$14$		−	1.00000i		−	0.267261i
$15$	0.820469	−	1.85634i	0.211844	−	0.479305i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−0.258842	−	0.448327i	−0.0627784	−	0.108735i	0.832928	−	0.553381i	$-0.186663\pi$
$17$	−0.258842	−	0.448327i	−0.0627784	−	0.108735i	−0.895706	+	0.444646i	$0.853329\pi$
$18$	−1.62024	+	2.52484i	−0.381895	+	0.595110i
$19$	5.50267	+	1.47444i	1.26240	+	0.338259i	0.827114	−	0.562034i	$-0.189981\pi$
$19$	5.50267	+	1.47444i	1.26240	+	0.338259i	0.435285	+	0.900293i	$0.356648\pi$
$20$	1.13185	+	0.303278i	0.253089	+	0.0678150i
$21$	−1.72206	+	0.185721i	−0.375785	+	0.0405276i
$22$	−2.41852	−	4.18900i	−0.515631	−	0.893098i
$23$	−2.54064	+	4.40052i	−0.529760	+	0.917572i	0.469637	+	0.882860i	$0.344385\pi$
$23$	−2.54064	+	4.40052i	−0.529760	+	0.917572i	−0.999397	+	0.0347123i	$0.988949\pi$
$24$	−1.58421	−	0.700193i	−0.323376	−	0.142926i
$25$		−	3.62694i		−	0.725389i
$26$	−0.864656	−	3.50034i	−0.169573	−	0.686473i
$27$	4.64885	+	2.32125i	0.894672	+	0.446724i
$28$	−0.258819	−	0.965926i	−0.0489122	−	0.182543i
$29$	1.83703	+	1.06061i	0.341129	+	0.196951i	0.660771	−	0.750588i	$-0.270229\pi$
$29$	1.83703	+	1.06061i	0.341129	+	0.196951i	−0.319642	+	0.947538i	$0.603563\pi$
$30$	0.312056	−	2.00544i	0.0569734	−	0.366142i
$31$	4.11077	−	4.11077i	0.738316	−	0.738316i	−0.233936	−	0.972252i	$-0.575161\pi$
$31$	4.11077	−	4.11077i	0.738316	−	0.738316i	0.972252	+	0.233936i	$0.0751607\pi$
$32$	0.258819	−	0.965926i	0.0457532	−	0.170753i
$33$	−6.76456	+	4.94284i	−1.17756	+	0.860438i
$34$	−0.366058	−	0.366058i	−0.0627784	−	0.0627784i
$35$	1.01479	−	0.585888i	0.171530	−	0.0990331i
$36$	−0.911557	+	2.85816i	−0.151926	+	0.476360i
$37$	−9.86282	+	2.64273i	−1.62144	+	0.434463i	−0.951423	−	0.307886i	$-0.900379\pi$
$37$	−9.86282	+	2.64273i	−1.62144	+	0.434463i	−0.670014	+	0.742349i	$0.733712\pi$
$38$	5.69678			0.924140
$39$	−5.86723	+	2.13908i	−0.939508	+	0.342527i
$40$	1.17178			0.185274
$41$	−6.46664	+	1.73273i	−1.00992	+	0.270607i	−0.725596	−	0.688121i	$-0.758436\pi$
$41$	−6.46664	+	1.73273i	−1.00992	+	0.270607i	−0.284324	+	0.958728i	$0.591769\pi$
$42$	−1.61532	+	0.625096i	−0.249249	+	0.0964544i
$43$	−0.253885	+	0.146580i	−0.0387170	+	0.0223533i	−0.519234	−	0.854632i	$-0.673783\pi$
$43$	−0.253885	+	0.146580i	−0.0387170	+	0.0223533i	0.480517	+	0.876986i	$0.340449\pi$
$44$	−3.42031	−	3.42031i	−0.515631	−	0.515631i
$45$	−3.51145	−	0.164928i	−0.523457	−	0.0245861i
$46$	−1.31513	+	4.90814i	−0.193906	+	0.723666i
$47$	8.54481	−	8.54481i	1.24639	−	1.24639i	0.289086	−	0.957303i	$-0.406649\pi$
$47$	8.54481	−	8.54481i	1.24639	−	1.24639i	0.957303	−	0.289086i	$-0.0933513\pi$
$48$	−1.71146	−	0.266310i	−0.247027	−	0.0384386i
$49$	−0.866025	−	0.500000i	−0.123718	−	0.0714286i
$50$	−0.938722	−	3.50336i	−0.132755	−	0.495450i
$51$	−0.562390	+	0.698360i	−0.0787504	+	0.0977899i
$52$	−1.74115	−	3.15728i	−0.241454	−	0.437836i
$53$			9.52725i			1.30867i	0.756206	+	0.654334i	$0.227051\pi$
$53$			9.52725i			1.30867i	−0.756206	+	0.654334i	$0.772949\pi$
$54$	5.09123	+	1.03894i	0.692828	+	0.141382i
$55$	2.83396	−	4.90857i	0.382132	−	0.661871i
$56$	−0.500000	−	0.866025i	−0.0668153	−	0.115728i
$57$	−1.05801	−	9.81023i	−0.140137	−	1.29940i
$58$	2.04895	+	0.549013i	0.269040	+	0.0720890i
$59$	1.53749	+	0.411970i	0.200164	+	0.0536339i	0.357508	−	0.933910i	$-0.383626\pi$
$59$	1.53749	+	0.411970i	0.200164	+	0.0536339i	−0.157344	+	0.987544i	$0.550293\pi$
$60$	−0.217623	−	2.01787i	−0.0280950	−	0.260506i
$61$	5.90367	+	10.2255i	0.755888	+	1.30924i	0.944932	+	0.327267i	$0.106128\pi$
$61$	5.90367	+	10.2255i	0.755888	+	1.30924i	−0.189044	+	0.981969i	$0.560539\pi$
$62$	2.90675	−	5.03464i	0.369158	−	0.639400i
$63$	1.37645	+	2.66559i	0.173417	+	0.335833i
$64$		−	1.00000i		−	0.125000i
$65$	3.04551	−	2.92825i	0.377749	−	0.363204i
$66$	−5.25477	+	6.52521i	−0.646817	+	0.803198i
$67$	2.99192	+	11.1660i	0.365521	+	1.36414i	0.866713	+	0.498807i	$0.166228\pi$
$67$	2.99192	+	11.1660i	0.365521	+	1.36414i	−0.501192	+	0.865336i	$0.667105\pi$
$68$	−0.448327	−	0.258842i	−0.0543677	−	0.0313892i
$69$	8.69639	+	1.35320i	1.04692	+	0.162906i
$70$	0.828570	−	0.828570i	0.0990331	−	0.0990331i
$71$	0.487312	−	1.81867i	0.0578332	−	0.215837i	−0.930962	−	0.365117i	$-0.881029\pi$
$71$	0.487312	−	1.81867i	0.0578332	−	0.215837i	0.988795	+	0.149280i	$0.0476957\pi$
$72$	−0.140751	+	2.99670i	−0.0165876	+	0.353164i
$73$	4.68386	+	4.68386i	0.548205	+	0.548205i	0.925921	−	0.377716i	$-0.123291\pi$
$73$	4.68386	+	4.68386i	0.548205	+	0.548205i	−0.377716	+	0.925921i	$0.623291\pi$
$74$	−8.84276	+	5.10537i	−1.02795	+	0.593487i
$75$	−5.85867	+	2.26719i	−0.676501	+	0.261792i
$76$	5.50267	−	1.47444i	0.631199	−	0.169129i
$77$	−4.83704			−0.551232
$78$	−5.11367	+	3.58474i	−0.579009	+	0.405892i
$79$	2.53289			0.284973			0.142486	−	0.989797i	$-0.454490\pi$
$79$	2.53289			0.284973			0.142486	+	0.989797i	$0.454490\pi$
$80$	1.13185	−	0.303278i	0.126544	−	0.0339075i
$81$	0.843575	−	8.96038i	0.0937305	−	0.995598i
$82$	−5.79783	+	3.34738i	−0.640263	+	0.369656i
$83$	11.7215	+	11.7215i	1.28660	+	1.28660i	0.936841	+	0.349756i	$0.113736\pi$
$83$	11.7215	+	11.7215i	1.28660	+	1.28660i	0.349756	+	0.936841i	$0.386264\pi$
$84$	−1.39849	+	1.02187i	−0.152588	+	0.111495i
$85$	0.157002	−	0.585939i	0.0170292	−	0.0635540i
$86$	−0.207296	+	0.207296i	−0.0223533	+	0.0223533i
$87$	0.564904	−	3.63038i	0.0605641	−	0.389218i
$88$	−4.18900	−	2.41852i	−0.446549	−	0.257815i
$89$	−0.717827	−	2.67897i	−0.0760895	−	0.283970i	0.917389	−	0.397993i	$-0.130293\pi$
$89$	−0.717827	−	2.67897i	−0.0760895	−	0.283970i	−0.993478	+	0.114023i	$0.963626\pi$
$90$	−3.43449	+	0.749523i	−0.362027	+	0.0790066i
$91$	−3.46371	−	1.00135i	−0.363095	−	0.104971i
$92$			5.08128i			0.529760i
$93$	−9.20983	−	4.07058i	−0.955015	−	0.422099i
$94$	6.04209	−	10.4652i	0.623194	−	1.07940i
$95$	3.33767	+	5.78102i	0.342438	+	0.593120i
$96$	−1.72206	+	0.185721i	−0.175758	+	0.0189551i
$97$	3.95229	+	1.05901i	0.401294	+	0.107526i	0.453821	−	0.891093i	$-0.350061\pi$
$97$	3.95229	+	1.05901i	0.401294	+	0.107526i	−0.0525264	+	0.998620i	$0.516727\pi$
$98$	−0.965926	−	0.258819i	−0.0975732	−	0.0261447i
$99$	12.2128	+	7.83718i	1.22743	+	0.787666i
$100$	−1.81347	−	3.14102i	−0.181347	−	0.314102i
$101$	1.81765	−	3.14826i	0.180863	−	0.313264i	−0.761312	−	0.648386i	$-0.775444\pi$
$101$	1.81765	−	3.14826i	0.180863	−	0.313264i	0.942175	+	0.335122i	$0.108778\pi$
$102$	−0.362479	+	0.820121i	−0.0358907	+	0.0812041i
$103$			13.3619i			1.31658i	0.752763	+	0.658292i	$0.228721\pi$
$103$			13.3619i			1.31658i	−0.752763	+	0.658292i	$0.771279\pi$
$104$	−2.49898	−	2.59905i	−0.245046	−	0.254858i
$105$	−1.58073	−	1.27297i	−0.154264	−	0.124229i
$106$	2.46583	+	9.20261i	0.239503	+	0.893837i
$107$	−1.29666	−	0.748627i	−0.125353	−	0.0723725i	0.436012	−	0.899941i	$-0.356390\pi$
$107$	−1.29666	−	0.748627i	−0.125353	−	0.0723725i	−0.561365	+	0.827568i	$0.689724\pi$
$108$	5.18665	−	0.314167i	0.499085	−	0.0302308i
$109$	−9.35366	+	9.35366i	−0.895918	+	0.895918i	−0.995072	−	0.0991537i	$-0.968386\pi$
$109$	−9.35366	+	9.35366i	−0.895918	+	0.895918i	0.0991537	+	0.995072i	$0.468386\pi$
$110$	1.46697	−	5.47480i	0.139870	−	0.522001i
$111$	10.4341	+	14.2796i	0.990358	+	1.35536i
$112$	−0.707107	−	0.707107i	−0.0668153	−	0.0668153i
$113$	14.8503	−	8.57383i	1.39700	−	0.806558i	0.402922	−	0.915234i	$-0.367995\pi$
$113$	14.8503	−	8.57383i	1.39700	−	0.806558i	0.994077	+	0.108676i	$0.0346612\pi$
$114$	−3.56103	−	9.20212i	−0.333521	−	0.861857i
$115$	−5.75124	+	1.54104i	−0.536306	+	0.143703i
$116$	2.12122			0.196951
$117$	7.12288	+	8.14031i	0.658510	+	0.752572i
$118$	1.59173			0.146530
$119$	−0.500044	+	0.133986i	−0.0458390	+	0.0122825i
$120$	−0.732472	−	1.89279i	−0.0668652	−	0.172787i
$121$	−10.7361	+	6.19850i	−0.976010	+	0.563500i
$122$	8.34905	+	8.34905i	0.755888	+	0.755888i
$123$	6.84118	+	9.36256i	0.616849	+	0.844194i
$124$	1.50465	−	5.61541i	0.135121	−	0.504279i
$125$	7.14803	−	7.14803i	0.639339	−	0.639339i
$126$	2.01946	+	2.21851i	0.179908	+	0.197641i
$127$	3.84030	+	2.21720i	0.340771	+	0.196744i	0.660613	−	0.750727i	$-0.270296\pi$
$127$	3.84030	+	2.21720i	0.340771	+	0.196744i	−0.319842	+	0.947471i	$0.603630\pi$
$128$	−0.258819	−	0.965926i	−0.0228766	−	0.0853766i
$129$	0.395476	+	0.318478i	0.0348197	+	0.0280404i
$130$	2.18385	−	3.61670i	0.191536	−	0.317206i
$131$		−	14.2928i		−	1.24877i	−0.781118	−	0.624384i	$-0.785350\pi$
$131$		−	14.2928i		−	1.24877i	0.781118	−	0.624384i	$-0.214650\pi$
$132$	−3.38687	+	7.66290i	−0.294789	+	0.666970i
$133$	2.84839	−	4.93356i	0.246987	−	0.427794i
$134$	5.77994	+	10.0112i	0.499311	+	0.864832i
$135$	1.92858	+	5.77521i	0.165986	+	0.497051i
$136$	−0.500044	−	0.133986i	−0.0428784	−	0.0114892i
$137$	9.27529	+	2.48531i	0.792441	+	0.212334i	0.632263	−	0.774754i	$-0.282126\pi$
$137$	9.27529	+	2.48531i	0.792441	+	0.212334i	0.160178	+	0.987088i	$0.448793\pi$
$138$	8.75030	−	0.943701i	0.744875	−	0.0803332i
$139$	−7.81211	−	13.5310i	−0.662615	−	1.14768i	−0.979926	−	0.199361i	$-0.936113\pi$
$139$	−7.81211	−	13.5310i	−0.662615	−	1.14768i	0.317312	−	0.948321i	$-0.397220\pi$
$140$	0.585888	−	1.01479i	0.0495165	−	0.0857652i
$141$	−19.1439	−	8.46127i	−1.61221	−	0.712567i
$142$		−	1.88283i		−	0.158003i
$143$	−16.9313	+	4.18238i	−1.41587	+	0.349748i
$144$	0.639647	+	2.93102i	0.0533039	+	0.244251i
$145$	0.643320	+	2.40090i	0.0534248	+	0.199384i
$146$	5.73654	+	3.31199i	0.474759	+	0.274102i
$147$	−0.266310	+	1.71146i	−0.0219649	+	0.141158i
$148$	−7.22008	+	7.22008i	−0.593487	+	0.593487i
$149$	1.69498	−	6.32574i	0.138858	−	0.518225i	−0.861094	−	0.508445i	$-0.830220\pi$
$149$	1.69498	−	6.32574i	0.138858	−	0.518225i	0.999952	−	0.00977946i	$-0.00311295\pi$
$150$	−5.07225	+	3.70627i	−0.414147	+	0.302616i
$151$	−15.6948	−	15.6948i	−1.27722	−	1.27722i	−0.942215	−	0.335009i	$-0.891260\pi$
$151$	−15.6948	−	15.6948i	−1.27722	−	1.27722i	−0.335009	−	0.942215i	$-0.608740\pi$
$152$	4.93356	−	2.84839i	0.400164	−	0.231035i
$153$	1.47962	+	0.471898i	0.119620	+	0.0381507i
$154$	−4.67223	+	1.25192i	−0.376499	+	0.100883i
$155$	6.81212			0.547163
$156$	−4.01163	+	4.78611i	−0.321187	+	0.383196i
$157$	−16.3039			−1.30119			−0.650597	−	0.759423i	$-0.725481\pi$
$157$	−16.3039			−1.30119			−0.650597	+	0.759423i	$0.725481\pi$
$158$	2.44659	−	0.655561i	0.194640	−	0.0521537i
$159$	15.3895	−	5.95544i	1.22047	−	0.472297i
$160$	1.01479	−	0.585888i	0.0802260	−	0.0463185i
$161$	3.59301	+	3.59301i	0.283169	+	0.283169i
$162$	−1.50429	−	8.87339i	−0.118188	−	0.697160i
$163$	−0.906537	+	3.38324i	−0.0710055	+	0.264996i	−0.992298	−	0.123874i	$-0.960468\pi$
$163$	−0.906537	+	3.38324i	−0.0710055	+	0.264996i	0.921292	+	0.388870i	$0.127135\pi$
$164$	−4.73391	+	4.73391i	−0.369656	+	0.369656i
$165$	−9.70040	−	1.50943i	−0.755175	−	0.117509i
$166$	14.3558	+	8.28832i	1.11423	+	0.643298i
$167$	3.88956	+	14.5160i	0.300983	+	1.12328i	0.936348	+	0.351072i	$0.114183\pi$
$167$	3.88956	+	14.5160i	0.300983	+	1.12328i	−0.635365	+	0.772212i	$0.719150\pi$
$168$	−1.08636	+	1.34901i	−0.0838144	+	0.104078i
$169$	−12.9900	−	0.510162i	−0.999230	−	0.0392432i
$170$		−	0.606609i		−	0.0465248i
$171$	−15.1853	+	7.84136i	−1.16125	+	0.599644i
$172$	−0.146580	+	0.253885i	−0.0111766	+	0.0193585i
$173$	−2.14061	−	3.70764i	−0.162748	−	0.281887i	0.773106	−	0.634277i	$-0.218702\pi$
$173$	−2.14061	−	3.70764i	−0.162748	−	0.281887i	−0.935853	+	0.352390i	$0.885369\pi$
$174$	−0.393956	−	3.65289i	−0.0298657	−	0.276925i
$175$	−3.50336	−	0.938722i	−0.264829	−	0.0709607i
$176$	−4.67223	−	1.25192i	−0.352182	−	0.0943669i
$177$	−0.295617	−	2.74106i	−0.0222200	−	0.206031i
$178$	−1.38673	−	2.40190i	−0.103940	−	0.180030i
$179$	5.33092	−	9.23342i	0.398452	−	0.690138i	−0.595084	−	0.803664i	$-0.702881\pi$
$179$	5.33092	−	9.23342i	0.398452	−	0.690138i	0.993535	+	0.113526i	$0.0362144\pi$
$180$	−3.12347	+	1.61290i	−0.232810	+	0.120218i
$181$			13.7234i			1.02005i	0.860160	+	0.510025i	$0.170364\pi$
$181$			13.7234i			1.02005i	−0.860160	+	0.510025i	$0.829636\pi$
$182$	−3.60486	−	0.0707604i	−0.267210	−	0.00524511i
$183$	12.8270	−	15.9282i	0.948200	−	1.17745i
$184$	1.31513	+	4.90814i	0.0969529	+	0.361833i
$185$	−10.3617	−	5.98235i	−0.761809	−	0.439831i
$186$	−9.94955	−	1.54820i	−0.729537	−	0.113519i
$187$	−1.77064	+	1.77064i	−0.129482	+	0.129482i
$188$	3.12762	−	11.6724i	0.228105	−	0.851299i
$189$	3.44536	−	3.88966i	0.250613	−	0.282931i
$190$	4.72018	+	4.72018i	0.342438	+	0.342438i
$191$	−15.7595	+	9.09873i	−1.14031	+	0.658361i	−0.946509	−	0.322679i	$-0.895417\pi$
$191$	−15.7595	+	9.09873i	−1.14031	+	0.658361i	−0.193806	+	0.981040i	$0.562083\pi$
$192$	−1.61532	+	0.625096i	−0.116576	+	0.0451124i
$193$	−0.834130	+	0.223505i	−0.0600420	+	0.0160882i	−0.288715	−	0.957415i	$-0.593228\pi$
$193$	−0.834130	+	0.223505i	−0.0600420	+	0.0160882i	0.228673	+	0.973503i	$0.426561\pi$
$194$	4.09171			0.293768
$195$	−6.63379	−	3.08903i	−0.475055	−	0.221210i
$196$	−1.00000			−0.0714286
$197$	−20.4357	+	5.47572i	−1.45598	+	0.390129i	−0.898100	−	0.439791i	$-0.855052\pi$
$197$	−20.4357	+	5.47572i	−1.45598	+	0.390129i	−0.557882	+	0.829920i	$0.688386\pi$
$198$	13.8250	+	4.40924i	0.982502	+	0.313351i
$199$	1.32932	−	0.767481i	0.0942327	−	0.0544053i	−0.452143	−	0.891945i	$-0.649340\pi$
$199$	1.32932	−	0.767481i	0.0942327	−	0.0544053i	0.546376	+	0.837540i	$0.316007\pi$
$200$	−2.56464	−	2.56464i	−0.181347	−	0.181347i
$201$	16.1664	−	11.8127i	1.14029	−	0.833205i
$202$	0.940885	−	3.51143i	0.0662004	−	0.247063i
$203$	1.49993	−	1.49993i	0.105275	−	0.105275i
$204$	−0.137865	+	0.885992i	−0.00965245	+	0.0620319i
$205$	−6.79375	−	3.92237i	−0.474496	−	0.273951i
$206$	3.45830	+	12.9066i	0.240951	+	0.899243i
$207$	−3.25023	−	14.8933i	−0.225907	−	1.03516i
$208$	−3.08652	−	1.86371i	−0.214011	−	0.129225i
$209$		−	27.5556i		−	1.90606i
$210$	−1.85634	−	0.820469i	−0.128100	−	0.0566178i
$211$	5.09230	−	8.82012i	0.350568	−	0.607202i	−0.635781	−	0.771870i	$-0.719322\pi$
$211$	5.09230	−	8.82012i	0.350568	−	0.607202i	0.986349	+	0.164668i	$0.0526551\pi$
$212$	4.76362	+	8.25084i	0.327167	+	0.566670i
$213$	−3.24235	+	0.349681i	−0.222162	+	0.0239597i
$214$	−1.44624	−	0.387518i	−0.0988626	−	0.0264902i
$215$	−0.331813	−	0.0889091i	−0.0226295	−	0.00606355i
$216$	4.92860	−	1.64587i	0.335349	−	0.111987i
$217$	−2.90675	−	5.03464i	−0.197323	−	0.341774i
$218$	−6.61404	+	11.4559i	−0.447959	+	0.775888i
$219$	4.63807	−	10.4938i	0.313412	−	0.709105i
$220$		−	5.66793i		−	0.382132i
$221$	−1.63447	+	0.901364i	−0.109946	+	0.0606323i
$222$	13.7744	+	11.0925i	0.924475	+	0.744482i
$223$	0.508845	+	1.89903i	0.0340748	+	0.127169i	0.980868	−	0.194673i	$-0.0623647\pi$
$223$	0.508845	+	1.89903i	0.0340748	+	0.127169i	−0.946793	+	0.321842i	$0.895698\pi$
$224$	−0.866025	−	0.500000i	−0.0578638	−	0.0334077i
$225$	7.32446	+	8.04641i	0.488297	+	0.536427i
$226$	12.1252	−	12.1252i	0.806558	−	0.806558i
$227$	−1.32281	+	4.93680i	−0.0877981	+	0.327667i	−0.995829	−	0.0912354i	$-0.970918\pi$
$227$	−1.32281	+	4.93680i	−0.0877981	+	0.327667i	0.908031	+	0.418903i	$0.137585\pi$
$228$	−5.82138	−	7.96690i	−0.385530	−	0.527621i
$229$	2.40035	+	2.40035i	0.158620	+	0.158620i	0.781955	−	0.623335i	$-0.214223\pi$
$229$	2.40035	+	2.40035i	0.158620	+	0.158620i	−0.623335	+	0.781955i	$0.714223\pi$
$230$	−5.15642	+	2.97706i	−0.340004	+	0.196302i
$231$	3.02362	+	7.81337i	0.198939	+	0.514082i
$232$	2.04895	−	0.549013i	0.134520	−	0.0360445i
$233$	−8.54899			−0.560063			−0.280032	−	0.959991i	$-0.590345\pi$
$233$	−8.54899			−0.560063			−0.280032	+	0.959991i	$0.590345\pi$
$234$	8.98704	+	6.01940i	0.587501	+	0.393500i
$235$	14.1600			0.923693
$236$	1.53749	−	0.411970i	0.100082	−	0.0268169i
$237$	−1.58330	−	4.09143i	−0.102847	−	0.265767i
$238$	−0.448327	+	0.258842i	−0.0290607	+	0.0167782i
$239$	20.0754	+	20.0754i	1.29857	+	1.29857i	0.929338	+	0.369230i	$0.120378\pi$
$239$	20.0754	+	20.0754i	1.29857	+	1.29857i	0.369230	+	0.929338i	$0.379622\pi$
$240$	−1.19740	−	1.63872i	−0.0772921	−	0.105779i
$241$	−5.75665	+	21.4841i	−0.370818	+	1.38391i	0.488542	+	0.872541i	$0.337529\pi$
$241$	−5.75665	+	21.4841i	−0.370818	+	1.38391i	−0.859360	+	0.511371i	$0.829138\pi$
$242$	−8.76600	+	8.76600i	−0.563500	+	0.563500i
$243$	−15.0012	+	4.23845i	−0.962326	+	0.271897i
$244$	10.2255	+	5.90367i	0.654618	+	0.377944i
$245$	−0.303278	−	1.13185i	−0.0193757	−	0.0723111i
$246$	9.03128	+	7.27291i	0.575814	+	0.463704i
$247$	5.70450	−	19.7320i	0.362969	−	1.25552i
$248$		−	5.81351i		−	0.369158i
$249$	11.6069	−	26.2609i	0.735555	−	1.66422i
$250$	5.05442	−	8.75451i	0.319670	−	0.553684i
$251$	−8.15438	−	14.1238i	−0.514700	−	0.891487i	−0.999854	−	0.0170582i	$-0.994570\pi$
$251$	−8.15438	−	14.1238i	−0.514700	−	0.891487i	0.485154	−	0.874429i	$-0.338763\pi$
$252$	2.52484	+	1.62024i	0.159050	+	0.102066i
$253$	23.7409	+	6.36136i	1.49258	+	0.399935i
$254$	4.28330	+	1.14771i	0.268758	+	0.0720135i
$255$	−1.04462	+	0.112660i	−0.0654166	+	0.00705504i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	1.49782	−	2.59430i	0.0934315	−	0.161828i	−0.815521	−	0.578727i	$-0.803550\pi$
$257$	1.49782	−	2.59430i	0.0934315	−	0.161828i	0.908953	+	0.416899i	$0.136883\pi$
$258$	0.464429	+	0.205269i	0.0289141	+	0.0127795i
$259$			10.2107i			0.634465i
$260$	1.17336	−	4.05869i	0.0727689	−	0.251709i
$261$	−6.21734	+	1.35684i	−0.384844	+	0.0839860i
$262$	−3.69925	−	13.8058i	−0.228540	−	0.852924i
$263$	−3.52497	−	2.03514i	−0.217359	−	0.125492i	0.387368	−	0.921925i	$-0.373384\pi$
$263$	−3.52497	−	2.03514i	−0.217359	−	0.125492i	−0.604727	+	0.796433i	$0.706718\pi$
$264$	−1.28816	+	8.27838i	−0.0792805	+	0.509499i
$265$	−7.89399	+	7.89399i	−0.484924	+	0.484924i
$266$	1.47444	−	5.50267i	0.0904034	−	0.337390i
$267$	−3.87867	+	2.83413i	−0.237371	+	0.173446i
$268$	8.17407	+	8.17407i	0.499311	+	0.499311i
$269$	2.68484	−	1.55010i	0.163698	−	0.0945110i	−0.415913	−	0.909404i	$-0.636538\pi$
$269$	2.68484	−	1.55010i	0.163698	−	0.0945110i	0.579611	+	0.814893i	$0.303205\pi$
$270$	3.35760	+	5.07927i	0.204337	+	0.309115i
$271$	14.8204	−	3.97111i	0.900275	−	0.241228i	0.221140	−	0.975242i	$-0.429022\pi$
$271$	14.8204	−	3.97111i	0.900275	−	0.241228i	0.679134	+	0.734014i	$0.262355\pi$
$272$	−0.517684			−0.0313892
$273$	0.547644	+	6.22094i	0.0331449	+	0.376508i
$274$	9.60248			0.580107
$275$	−16.9459	+	4.54064i	−1.02188	+	0.273811i
$276$	8.20789	−	3.17629i	0.494057	−	0.191190i
$277$	−1.05278	+	0.607822i	−0.0632553	+	0.0365205i	−0.531294	−	0.847187i	$-0.678294\pi$
$277$	−1.05278	+	0.607822i	−0.0632553	+	0.0365205i	0.468039	+	0.883708i	$0.344961\pi$
$278$	−11.0480	−	11.0480i	−0.662615	−	0.662615i
$279$	−0.818255	+	17.4213i	−0.0489877	+	1.04299i
$280$	0.303278	−	1.13185i	0.0181243	−	0.0676408i
$281$	−1.81570	+	1.81570i	−0.108316	+	0.108316i	−0.759188	−	0.650872i	$-0.774403\pi$
$281$	−1.81570	+	1.81570i	−0.108316	+	0.108316i	0.650872	+	0.759188i	$0.274403\pi$
$282$	−20.6815	−	3.21815i	−1.23157	−	0.191638i
$283$	−8.30363	−	4.79410i	−0.493600	−	0.284980i	0.232467	−	0.972604i	$-0.425320\pi$
$283$	−8.30363	−	4.79410i	−0.493600	−	0.284980i	−0.726067	+	0.687624i	$0.758654\pi$
$284$	−0.487312	−	1.81867i	−0.0289166	−	0.107918i
$285$	7.25182	−	9.00510i	0.429561	−	0.533416i
$286$	−15.2719	+	8.42201i	−0.903046	+	0.498004i
$287$			6.69476i			0.395179i
$288$	1.37645	+	2.66559i	0.0811084	+	0.157071i
$289$	8.36600	−	14.4903i	0.492118	−	0.852373i
$290$	1.24280	+	2.15259i	0.0729797	+	0.126405i
$291$	−0.759917	−	7.04619i	−0.0445471	−	0.413055i
$292$	6.39828	+	1.71441i	0.374431	+	0.100328i
$293$	−20.3586	−	5.45507i	−1.18936	−	0.318689i	−0.390729	−	0.920506i	$-0.627777\pi$
$293$	−20.3586	−	5.45507i	−1.18936	−	0.318689i	−0.798634	+	0.601817i	$0.794444\pi$
$294$	0.185721	+	1.72206i	0.0108315	+	0.100433i
$295$	0.932574	+	1.61527i	0.0542966	+	0.0940444i
$296$	−5.10537	+	8.84276i	−0.296744	+	0.513975i
$297$	5.02540	−	24.6265i	0.291603	−	1.42897i
$298$		−	6.54889i		−	0.379367i
$299$	15.6835	+	9.47003i	0.906998	+	0.547666i
$300$	−3.94016	+	4.89278i	−0.227485	+	0.282485i
$301$	0.0758756	+	0.283171i	0.00437339	+	0.0163217i
$302$	−19.2221	−	11.0979i	−1.10611	−	0.638612i
$303$	−6.22165	−	0.968119i	−0.357425	−	0.0556170i
$304$	4.02823	−	4.02823i	0.231035	−	0.231035i
$305$	−3.58090	+	13.3641i	−0.205042	+	0.765227i
$306$	1.55134	+	0.0728644i	0.0886842	+	0.00416538i
$307$	−1.05726	−	1.05726i	−0.0603413	−	0.0603413i	0.676292	−	0.736633i	$-0.263586\pi$
$307$	−1.05726	−	1.05726i	−0.0603413	−	0.0603413i	−0.736633	+	0.676292i	$0.763586\pi$
$308$	−4.18900	+	2.41852i	−0.238691	+	0.137808i
$309$	21.5837	−	8.35244i	1.22785	−	0.475154i
$310$	6.58000	−	1.76311i	0.373719	−	0.100138i
$311$	−6.32744			−0.358796			−0.179398	−	0.983777i	$-0.557415\pi$
$311$	−6.32744			−0.358796			−0.179398	+	0.983777i	$0.557415\pi$
$312$	−2.63620	+	5.66131i	−0.149245	+	0.320509i
$313$	−26.7529			−1.51216			−0.756081	−	0.654478i	$-0.772888\pi$
$313$	−26.7529			−1.51216			−0.756081	+	0.654478i	$0.772888\pi$
$314$	−15.7484	+	4.21977i	−0.888733	+	0.238135i
$315$	−1.06814	+	3.34912i	−0.0601829	+	0.188701i
$316$	2.19355	−	1.26645i	0.123397	−	0.0712432i
$317$	13.6159	+	13.6159i	0.764748	+	0.764748i	0.977177	−	0.212429i	$-0.0681374\pi$
$317$	13.6159	+	13.6159i	0.764748	+	0.764748i	−0.212429	+	0.977177i	$0.568137\pi$
$318$	13.3238	−	9.73562i	0.747160	−	0.545947i
$319$	2.65560	−	9.91084i	0.148685	−	0.554900i
$320$	0.828570	−	0.828570i	0.0463185	−	0.0463185i
$321$	−0.398734	+	2.56248i	−0.0222552	+	0.143024i
$322$	4.40052	+	2.54064i	0.245231	+	0.141584i
$323$	−0.763291	−	2.84864i	−0.0424707	−	0.158503i
$324$	−3.74963	−	8.18170i	−0.208313	−	0.454539i
$325$	−13.0746	−	0.256644i	−0.725249	−	0.0142360i
$326$			3.50259i			0.193991i
$327$	20.9561	+	9.26221i	1.15887	+	0.512201i
$328$	−3.34738	+	5.79783i	−0.184828	+	0.320132i
$329$	−6.04209	−	10.4652i	−0.333111	−	0.576966i
$330$	−9.76054	+	1.05265i	−0.537300	+	0.0579467i
$331$	−9.03418	−	2.42070i	−0.496564	−	0.133054i	0.00184113	−	0.999998i	$-0.499414\pi$
$331$	−9.03418	−	2.42070i	−0.496564	−	0.133054i	−0.498405	+	0.866945i	$0.666081\pi$
$332$	16.0118	+	4.29035i	0.878762	+	0.235464i
$333$	16.5439	−	25.7805i	0.906598	−	1.41276i
$334$	7.51405	+	13.0147i	0.411151	+	0.712134i
$335$	−6.77279	+	11.7308i	−0.370037	+	0.640923i
$336$	−0.700193	+	1.58421i	−0.0381987	+	0.0864259i
$337$			4.47748i			0.243904i	0.992536	+	0.121952i	$0.0389154\pi$
$337$			4.47748i			0.243904i	−0.992536	+	0.121952i	$0.961085\pi$
$338$	−12.6794	+	2.86928i	−0.689669	+	0.156068i
$339$	−23.1323	−	18.6285i	−1.25638	−	1.01176i
$340$	−0.157002	−	0.585939i	−0.00851462	−	0.0317770i
$341$	−24.3528	−	14.0601i	−1.31878	−	0.761396i
$342$	−12.6384	+	11.5044i	−0.683405	+	0.622087i
$343$	−0.707107	+	0.707107i	−0.0381802	+	0.0381802i
$344$	−0.0758756	+	0.283171i	−0.00409094	+	0.0152676i
$345$	6.08435	+	8.32679i	0.327570	+	0.448299i
$346$	−3.02728	−	3.02728i	−0.162748	−	0.162748i
$347$	−19.0489	+	10.9979i	−1.02260	+	0.590398i	−0.914856	−	0.403781i	$-0.867696\pi$
$347$	−19.0489	+	10.9979i	−1.02260	+	0.590398i	−0.107743	+	0.994179i	$0.534363\pi$
$348$	−1.32597	−	3.42645i	−0.0710794	−	0.183677i
$349$	34.1495	−	9.15032i	1.82798	−	0.489805i	0.830263	−	0.557371i	$-0.188190\pi$
$349$	34.1495	−	9.15032i	1.82798	−	0.489805i	0.997715	+	0.0675659i	$0.0215233\pi$
$350$	−3.62694			−0.193868
$351$	8.69671	−	16.5942i	0.464196	−	0.885732i
$352$	−4.83704			−0.257815
$353$	2.94177	−	0.788246i	0.156575	−	0.0419541i	−0.179680	−	0.983725i	$-0.557506\pi$
$353$	2.94177	−	0.788246i	0.156575	−	0.0419541i	0.336255	+	0.941771i	$0.390840\pi$
$354$	−0.994983	−	2.57115i	−0.0528827	−	0.136655i
$355$	1.91067	−	1.10313i	0.101408	−	0.0585478i
$356$	−1.96114	−	1.96114i	−0.103940	−	0.103940i
$357$	0.529006	+	0.723976i	0.0279980	+	0.0383169i
$358$	2.75949	−	10.2985i	0.145843	−	0.544295i
$359$	8.69884	−	8.69884i	0.459107	−	0.459107i	−0.439255	−	0.898362i	$-0.644758\pi$
$359$	8.69884	−	8.69884i	0.459107	−	0.459107i	0.898362	+	0.439255i	$0.144758\pi$
$360$	−2.59960	+	2.36635i	−0.137011	+	0.124718i
$361$	11.6509	+	6.72666i	0.613206	+	0.354035i
$362$	3.55187	+	13.2558i	0.186682	+	0.696707i
$363$	16.7236	+	13.4676i	0.877764	+	0.706865i
$364$	−3.50034	+	0.864656i	−0.183468	+	0.0453203i
$365$			7.76182i			0.406272i
$366$	8.26742	−	18.7053i	0.432145	−	0.977744i
$367$	7.85537	−	13.6059i	0.410047	−	0.710222i	−0.584847	−	0.811143i	$-0.698846\pi$
$367$	7.85537	−	13.6059i	0.410047	−	0.710222i	0.994894	+	0.100921i	$0.0321789\pi$
$368$	2.54064	+	4.40052i	0.132440	+	0.229393i
$369$	10.8471	−	16.9032i	0.564679	−	0.879945i
$370$	−11.5570	−	3.09669i	−0.600820	−	0.160989i
$371$	9.20261	+	2.46583i	0.477776	+	0.128020i
$372$	−10.0112	+	1.07969i	−0.519058	+	0.0559793i
$373$	−1.05627	−	1.82952i	−0.0546918	−	0.0947290i	0.837383	−	0.546616i	$-0.184084\pi$
$373$	−1.05627	−	1.82952i	−0.0546918	−	0.0947290i	−0.892075	+	0.451887i	$0.850751\pi$
$374$	−1.25203	+	2.16858i	−0.0647409	+	0.112135i
$375$	−16.0145	−	7.07814i	−0.826988	−	0.365514i
$376$		−	12.0842i		−	0.623194i
$377$	3.95334	−	6.54720i	0.203608	−	0.337198i
$378$	2.32125	−	4.64885i	0.119392	−	0.239111i
$379$	−8.89975	−	33.2143i	−0.457150	−	1.70611i	−0.681690	−	0.731641i	$-0.738755\pi$
$379$	−8.89975	−	33.2143i	−0.457150	−	1.70611i	0.224540	−	0.974465i	$-0.427912\pi$
$380$	5.78102	+	3.33767i	0.296560	+	0.171219i
$381$	1.18093	−	7.58927i	0.0605007	−	0.388810i
$382$	−12.8675	+	12.8675i	−0.658361	+	0.658361i
$383$	7.20127	−	26.8755i	0.367968	−	1.37327i	−0.495385	−	0.868673i	$-0.664973\pi$
$383$	7.20127	−	26.8755i	0.367968	−	1.37327i	0.863353	−	0.504600i	$-0.168360\pi$
$384$	−1.39849	+	1.02187i	−0.0713665	+	0.0521472i
$385$	−4.00783	−	4.00783i	−0.204258	−	0.204258i
$386$	−0.747861	+	0.431778i	−0.0380651	+	0.0219769i
$387$	0.267233	−	0.837899i	0.0135842	−	0.0425928i
$388$	3.95229	−	1.05901i	0.200647	−	0.0537632i
$389$	16.0139			0.811938			0.405969	−	0.913887i	$-0.366934\pi$
$389$	16.0139			0.811938			0.405969	+	0.913887i	$0.366934\pi$
$390$	−7.20725	−	1.26682i	−0.364953	−	0.0641481i
$391$	2.63050			0.133030
$392$	−0.965926	+	0.258819i	−0.0487866	+	0.0130723i
$393$	−23.0874	+	8.93437i	−1.16461	+	0.450679i
$394$	−18.3221	+	10.5783i	−0.923056	+	0.532926i
$395$	2.09868	+	2.09868i	0.105596	+	0.105596i
$396$	14.4952	+	0.680818i	0.728409	+	0.0342124i
$397$	−3.61458	+	13.4898i	−0.181411	+	0.677034i	0.813960	+	0.580921i	$0.197308\pi$
$397$	−3.61458	+	13.4898i	−0.181411	+	0.677034i	−0.995370	+	0.0961128i	$0.969359\pi$
$398$	1.08538	−	1.08538i	0.0544053	−	0.0544053i
$399$	−9.74979	−	1.51711i	−0.488100	−	0.0759506i
$400$	−3.14102	−	1.81347i	−0.157051	−	0.0906736i
$401$	−6.69859	−	24.9995i	−0.334512	−	1.24841i	−0.904398	−	0.426691i	$-0.859679\pi$
$401$	−6.69859	−	24.9995i	−0.334512	−	1.24841i	0.569886	−	0.821724i	$-0.306987\pi$
$402$	12.5582	−	15.5944i	0.626346	−	0.777777i
$403$	−14.5279	−	15.1096i	−0.723684	−	0.752663i
$404$		−	3.63530i		−	0.180863i
$405$	8.12326	−	6.72534i	0.403648	−	0.334185i
$406$	1.06061	−	1.83703i	0.0526373	−	0.0911705i
$407$	24.6949	+	42.7728i	1.22408	+	2.12017i
$408$	0.0961447	+	0.891485i	0.00475987	+	0.0441351i
$409$	7.28579	+	1.95222i	0.360259	+	0.0965311i	0.434408	−	0.900716i	$-0.356958\pi$
$409$	7.28579	+	1.95222i	0.360259	+	0.0965311i	−0.0741494	+	0.997247i	$0.523624\pi$
$410$	−7.57745	−	2.03037i	−0.374223	−	0.100273i
$411$	−1.78338	−	16.5361i	−0.0879678	−	0.815666i
$412$	6.68093	+	11.5717i	0.329146	+	0.570097i
$413$	0.795864	−	1.37848i	0.0391619	−	0.0678304i
$414$	−6.99415	−	13.5446i	−0.343744	−	0.665682i
$415$			19.4241i			0.953491i
$416$	−3.46371	−	1.00135i	−0.169822	−	0.0490955i
$417$	−16.9735	+	21.0772i	−0.831197	+	1.03216i
$418$	−7.13191	−	26.6166i	−0.348833	−	1.30186i
$419$	−14.3943	−	8.31054i	−0.703206	−	0.405996i	0.105334	−	0.994437i	$-0.466409\pi$
$419$	−14.3943	−	8.31054i	−0.703206	−	0.405996i	−0.808541	+	0.588440i	$0.799742\pi$
$420$	−2.00544	−	0.312056i	−0.0978555	−	0.0152268i
$421$	−8.80780	+	8.80780i	−0.429266	+	0.429266i	−0.888378	−	0.459112i	$-0.848168\pi$
$421$	−8.80780	+	8.80780i	−0.429266	+	0.429266i	0.459112	+	0.888378i	$0.348168\pi$
$422$	2.63597	−	9.83757i	0.128317	−	0.478885i
$423$	−1.70086	+	36.2126i	−0.0826986	+	1.76072i
$424$	6.73678	+	6.73678i	0.327167	+	0.327167i
$425$	−1.62606	+	0.938805i	−0.0788754	+	0.0455387i
$426$	−3.04137	+	1.17695i	−0.147355	+	0.0570233i
$427$	11.4050	−	3.05596i	0.551927	−	0.147888i
$428$	−1.49725			−0.0723725
$429$	17.3396	+	24.7350i	0.837162	+	1.19422i
$430$	−0.343518			−0.0165659
$431$	−18.4277	+	4.93767i	−0.887629	+	0.237839i	−0.673696	−	0.739009i	$-0.735294\pi$
$431$	−18.4277	+	4.93767i	−0.887629	+	0.237839i	−0.213933	+	0.976848i	$0.568627\pi$
$432$	4.33468	−	2.86540i	0.208553	−	0.137862i
$433$	−17.4264	+	10.0611i	−0.837458	+	0.483507i	−0.856399	−	0.516314i	$-0.827304\pi$
$433$	−17.4264	+	10.0611i	−0.837458	+	0.483507i	0.0189413	+	0.999821i	$0.493970\pi$
$434$	−4.11077	−	4.11077i	−0.197323	−	0.197323i
$435$	3.47609	−	2.53996i	0.166666	−	0.121782i
$436$	−3.42368	+	12.7773i	−0.163964	+	0.611924i
$437$	−20.4686	+	20.4686i	−0.979146	+	0.979146i
$438$	1.76404	−	11.3367i	0.0842889	−	0.541686i
$439$	22.2565	+	12.8498i	1.06225	+	0.613288i	0.926052	−	0.377395i	$-0.123180\pi$
$439$	22.2565	+	12.8498i	1.06225	+	0.613288i	0.136193	+	0.990682i	$0.456513\pi$
$440$	−1.46697	−	5.47480i	−0.0699349	−	0.261001i
$441$	2.93102	−	0.639647i	0.139572	−	0.0304594i
$442$	−1.34549	+	1.29368i	−0.0639983	+	0.0615342i
$443$			0.0356586i			0.00169419i	1.00000		0.000847095i	$0.000269639\pi$
$443$			0.0356586i			0.00169419i	−1.00000		0.000847095i	$0.999730\pi$
$444$	16.1760	+	7.14949i	0.767678	+	0.339300i
$445$	1.62494	−	2.81448i	0.0770296	−	0.133419i
$446$	0.983012	+	1.70263i	0.0465470	+	0.0806217i
$447$	−11.2776	+	1.21627i	−0.533413	+	0.0575274i
$448$	−0.965926	−	0.258819i	−0.0456357	−	0.0122281i
$449$	26.1123	+	6.99677i	1.23231	+	0.330198i	0.815480	−	0.578785i	$-0.196473\pi$
$449$	26.1123	+	6.99677i	1.23231	+	0.330198i	0.416834	+	0.908982i	$0.363139\pi$
$450$	9.15745	+	5.87653i	0.431686	+	0.277022i
$451$	16.1914	+	28.0444i	0.762424	+	1.32056i
$452$	8.57383	−	14.8503i	0.403279	−	0.698500i
$453$	−15.5413	+	35.1628i	−0.730196	+	1.65209i
$454$			5.11095i			0.239869i
$455$	−2.04023	−	3.69962i	−0.0956477	−	0.173441i
$456$	−7.68501	−	6.18875i	−0.359883	−	0.289815i
$457$	−8.04660	−	30.0303i	−0.376404	−	1.40476i	−0.851282	−	0.524708i	$-0.824174\pi$
$457$	−8.04660	−	30.0303i	−0.376404	−	1.40476i	0.474878	−	0.880052i	$-0.342492\pi$
$458$	2.93982	+	1.69731i	0.137369	+	0.0793099i
$459$	−0.162639	−	2.68504i	−0.00759135	−	0.125327i
$460$	−4.21020	+	4.21020i	−0.196302	+	0.196302i
$461$	4.89115	−	18.2540i	0.227804	−	0.850174i	−0.753458	−	0.657496i	$-0.771616\pi$
$461$	4.89115	−	18.2540i	0.227804	−	0.850174i	0.981262	−	0.192679i	$-0.0617175\pi$
$462$	4.94284	+	6.76456i	0.229962	+	0.314716i
$463$	0.959289	+	0.959289i	0.0445819	+	0.0445819i	0.729046	−	0.684464i	$-0.239964\pi$
$463$	0.959289	+	0.959289i	0.0445819	+	0.0445819i	−0.684464	+	0.729046i	$0.739964\pi$
$464$	1.83703	−	1.06061i	0.0852822	−	0.0492377i
$465$	−4.25823	−	11.0037i	−0.197471	−	0.510287i
$466$	−8.25769	+	2.21264i	−0.382530	+	0.102499i
$467$	−28.3194			−1.31046			−0.655232	−	0.755428i	$-0.727429\pi$
$467$	−28.3194			−1.31046			−0.655232	+	0.755428i	$0.727429\pi$
$468$	10.2387	+	3.48828i	0.473286	+	0.161246i
$469$	11.5599			0.533786
$470$	13.6775	−	3.66487i	0.630894	−	0.169048i
$471$	10.1915	+	26.3360i	0.469600	+	1.21350i
$472$	1.37848	−	0.795864i	0.0634496	−	0.0366326i
$473$	1.00270	+	1.00270i	0.0461042	+	0.0461042i
$474$	−2.58829	−	3.54223i	−0.118884	−	0.162700i
$475$	5.34769	−	19.9579i	0.245369	−	0.915730i
$476$	−0.366058	+	0.366058i	−0.0167782	+	0.0167782i
$477$	−19.2399	−	21.1363i	−0.880934	−	0.967765i
$478$	24.5872	+	14.1954i	1.12459	+	0.649284i
$479$	5.48863	+	20.4838i	0.250782	+	0.935930i	0.970389	+	0.241549i	$0.0776553\pi$
$479$	5.48863	+	20.4838i	0.250782	+	0.935930i	−0.719607	+	0.694382i	$0.755678\pi$
$480$	−1.58073	−	1.27297i	−0.0721503	−	0.0581028i
$481$	8.82878	+	35.7410i	0.402558	+	1.62965i
$482$			22.2420i			1.01309i
$483$	3.55788	−	8.04983i	0.161889	−	0.366280i
$484$	−6.19850	+	10.7361i	−0.281750	+	0.488005i
$485$	2.39728	+	4.15222i	0.108855	+	0.188542i
$486$	−13.3930	+	7.97662i	−0.607521	+	0.361827i
$487$	25.2906	+	6.77660i	1.14603	+	0.307077i	0.781372	−	0.624066i	$-0.214520\pi$
$487$	25.2906	+	6.77660i	1.14603	+	0.307077i	0.364655	+	0.931143i	$0.381187\pi$
$488$	11.4050	+	3.05596i	0.516281	+	0.138337i
$489$	6.03169	−	0.650505i	0.272762	−	0.0294168i
$490$	−0.585888	−	1.01479i	−0.0264677	−	0.0458434i
$491$	−5.30462	+	9.18788i	−0.239394	+	0.414643i	−0.960541	−	0.278140i	$-0.910282\pi$
$491$	−5.30462	+	9.18788i	−0.239394	+	0.414643i	0.721146	+	0.692783i	$0.243616\pi$
$492$	10.6059	+	4.68762i	0.478152	+	0.211334i
$493$		−	1.09812i		−	0.0494570i
$494$	0.403106	−	20.5361i	0.0181366	−	0.923962i
$495$	3.62547	+	16.6128i	0.162953	+	0.746689i
$496$	−1.50465	−	5.61541i	−0.0675606	−	0.252140i
$497$	−1.63058	−	0.941414i	−0.0731413	−	0.0422282i
$498$	4.41453	−	28.3702i	0.197820	−	1.27130i
$499$	−23.7488	+	23.7488i	−1.06314	+	1.06314i	−0.0652762	+	0.997867i	$0.520793\pi$
$499$	−23.7488	+	23.7488i	−1.06314	+	1.06314i	−0.997867	+	0.0652762i	$0.979207\pi$
$500$	2.61636	−	9.76439i	0.117007	−	0.436677i
$501$	21.0167	−	15.3568i	0.938956	−	0.686091i
$502$	−11.5320	−	11.5320i	−0.514700	−	0.514700i
$503$	10.3733	−	5.98900i	0.462520	−	0.267036i	−0.250583	−	0.968095i	$-0.580622\pi$
$503$	10.3733	−	5.98900i	0.462520	−	0.267036i	0.713103	+	0.701059i	$0.247289\pi$
$504$	2.85816	+	0.911557i	0.127312	+	0.0406040i
$505$	4.11461	−	1.10251i	0.183098	−	0.0490609i
$506$	24.5784			1.09264
$507$	7.29591	+	21.3019i	0.324023	+	0.946049i
$508$	4.43439			0.196744
$509$	−3.78952	+	1.01540i	−0.167967	+	0.0450067i	−0.341823	−	0.939764i	$-0.611044\pi$
$509$	−3.78952	+	1.01540i	−0.167967	+	0.0450067i	0.173855	+	0.984771i	$0.444378\pi$
$510$	−0.979867	+	0.379189i	−0.0433892	+	0.0167908i
$511$	5.73654	−	3.31199i	0.253770	−	0.146514i
$512$	−0.707107	−	0.707107i	−0.0312500	−	0.0312500i
$513$	22.1586	+	19.6275i	0.978324	+	0.866574i
$514$	0.775329	−	2.89357i	0.0341983	−	0.127630i
$515$	−11.0712	+	11.0712i	−0.487857	+	0.487857i
$516$	0.501731	+	0.0780718i	0.0220875	+	0.00343692i
$517$	−50.6207	−	29.2259i	−2.22630	−	1.28535i
$518$	2.64273	+	9.86282i	0.116115	+	0.433347i
$519$	−4.65094	+	5.77540i	−0.204154	+	0.253512i
$520$	0.0829152	−	4.22408i	0.00363607	−	0.185238i
$521$		−	0.453994i		−	0.0198899i	−0.999951	−	0.00994493i	$-0.996834\pi$
$521$		−	0.453994i		−	0.0198899i	0.999951	−	0.00994493i	$-0.00316562\pi$
$522$	−5.65432	+	2.91977i	−0.247483	+	0.127795i
$523$	3.82939	−	6.63269i	0.167447	−	0.290027i	−0.770074	−	0.637954i	$-0.779781\pi$
$523$	3.82939	−	6.63269i	0.167447	−	0.290027i	0.937522	+	0.347927i	$0.113114\pi$
$524$	−7.14640	−	12.3779i	−0.312192	−	0.540732i
$525$	0.673600	+	6.24583i	0.0293983	+	0.272590i
$526$	−3.93159	−	1.05347i	−0.171425	−	0.0459333i
$527$	−2.90701	−	0.778931i	−0.126631	−	0.0339307i
$528$	0.898341	+	8.32970i	0.0390953	+	0.362504i
$529$	−1.40972	−	2.44171i	−0.0612922	−	0.106161i
$530$	−5.58190	+	9.66813i	−0.242462	+	0.419957i
$531$	−4.24290	+	2.19094i	−0.184126	+	0.0950788i
$532$		−	5.69678i		−	0.246987i
$533$	5.78866	+	23.4339i	0.250735	+	1.01504i
$534$	−3.01298	+	3.74143i	−0.130385	+	0.161908i
$535$	−0.454083	−	1.69466i	−0.0196317	−	0.0732667i
$536$	10.0112	+	5.77994i	0.432416	+	0.249656i
$537$	−18.2473	−	2.83936i	−0.787427	−	0.122527i
$538$	2.19217	−	2.19217i	0.0945110	−	0.0945110i
$539$	−1.25192	+	4.67223i	−0.0539240	+	0.201247i
$540$	4.55781	+	4.03719i	0.196137	+	0.173733i
$541$	13.2203	+	13.2203i	0.568384	+	0.568384i	0.931676	−	0.363291i	$-0.118347\pi$
$541$	13.2203	+	13.2203i	0.568384	+	0.568384i	−0.363291	+	0.931676i	$0.618347\pi$
$542$	13.2876	−	7.67160i	0.570751	−	0.329523i
$543$	22.1676	−	8.57842i	0.951304	−	0.368135i
$544$	−0.500044	+	0.133986i	−0.0214392	+	0.00574462i
$545$	−15.5003			−0.663961
$546$	2.13908	+	5.86723i	0.0915442	+	0.251094i
$547$	−12.2763			−0.524896			−0.262448	−	0.964946i	$-0.584530\pi$
$547$	−12.2763			−0.524896			−0.262448	+	0.964946i	$0.584530\pi$
$548$	9.27529	−	2.48531i	0.396221	−	0.106167i
$549$	−33.7472	−	10.7631i	−1.44030	−	0.459356i
$550$	−15.1933	+	8.77184i	−0.647843	+	0.374033i
$551$	8.54479	+	8.54479i	0.364020	+	0.364020i
$552$	7.10613	−	5.19242i	0.302457	−	0.221004i
$553$	0.655561	−	2.44659i	0.0278773	−	0.104040i
$554$	−0.859590	+	0.859590i	−0.0365205	+	0.0365205i
$555$	−3.18632	+	20.4770i	−0.135252	+	0.869202i
$556$	−13.5310	−	7.81211i	−0.573841	−	0.331307i
$557$	7.35055	+	27.4326i	0.311453	+	1.16236i	0.927247	+	0.374450i	$0.122169\pi$
$557$	7.35055	+	27.4326i	0.311453	+	1.16236i	−0.615794	+	0.787907i	$0.711165\pi$
$558$	3.71859	+	17.0395i	0.157421	+	0.721338i
$559$	0.510436	+	0.925590i	0.0215891	+	0.0391483i
$560$		−	1.17178i		−	0.0495165i
$561$	3.96696	+	1.75333i	0.167485	+	0.0740254i
$562$	−1.28389	+	2.22377i	−0.0541578	+	0.0938041i
$563$	4.58399	+	7.93971i	0.193192	+	0.334619i	0.946306	−	0.323271i	$-0.104783\pi$
$563$	4.58399	+	7.93971i	0.193192	+	0.334619i	−0.753114	+	0.657890i	$0.771449\pi$
$564$	−20.8098	+	2.24429i	−0.876249	+	0.0945016i
$565$	19.4085	+	5.20050i	0.816523	+	0.218787i
$566$	−9.26150	−	2.48161i	−0.389290	−	0.104310i
$567$	−8.43673	−	3.13395i	−0.354309	−	0.131613i
$568$	−0.941414	−	1.63058i	−0.0395008	−	0.0684175i
$569$	9.38211	−	16.2503i	0.393319	−	0.681248i	−0.599566	−	0.800325i	$-0.704660\pi$
$569$	9.38211	−	16.2503i	0.393319	−	0.681248i	0.992885	+	0.119077i	$0.0379936\pi$
$570$	4.67403	−	10.5752i	0.195774	−	0.442945i
$571$			40.4283i			1.69187i	0.533285	+	0.845936i	$0.320957\pi$
$571$			40.4283i			1.69187i	−0.533285	+	0.845936i	$0.679043\pi$
$572$	−12.5717	+	12.0877i	−0.525651	+	0.505412i
$573$	24.5485	+	19.7690i	1.02553	+	0.825861i
$574$	1.73273	+	6.46664i	0.0723228	+	0.269912i
$575$	15.9604	+	9.21476i	0.665596	+	0.384282i
$576$	2.01946	+	2.21851i	0.0841441	+	0.0924379i
$577$	19.6981	−	19.6981i	0.820041	−	0.820041i	−0.166073	−	0.986114i	$-0.553109\pi$
$577$	19.6981	−	19.6981i	0.820041	−	0.820041i	0.986114	+	0.166073i	$0.0531086\pi$
$578$	4.33056	−	16.1619i	0.180128	−	0.672245i
$579$	0.882442	+	1.20767i	0.0366731	+	0.0501892i
$580$	1.75758	+	1.75758i	0.0729797	+	0.0729797i
$581$	14.3558	−	8.28832i	0.595579	−	0.343857i
$582$	−2.55771	−	6.60942i	−0.106021	−	0.273969i
$583$	44.5134	−	11.9273i	1.84356	−	0.493980i
$584$	6.62398			0.274102
$585$	−0.843015	+	12.6466i	−0.0348544	+	0.522873i
$586$	−21.0768			−0.870674
$587$	−6.77509	+	1.81538i	−0.279638	+	0.0749288i	−0.395912	−	0.918288i	$-0.629572\pi$
$587$	−6.77509	+	1.81538i	−0.279638	+	0.0749288i	0.116274	+	0.993217i	$0.462905\pi$
$588$	0.625096	+	1.61532i	0.0257785	+	0.0666146i
$589$	28.6813	−	16.5591i	1.18179	−	0.682307i
$590$	1.31886	+	1.31886i	0.0542966	+	0.0542966i
$591$	21.6193	+	29.5873i	0.889299	+	1.21706i
$592$	−2.64273	+	9.86282i	−0.108616	+	0.405359i
$593$	−11.2191	+	11.2191i	−0.460714	+	0.460714i	−0.898890	−	0.438175i	$-0.855625\pi$
$593$	−11.2191	+	11.2191i	−0.460714	+	0.460714i	0.438175	+	0.898890i	$0.355625\pi$
$594$	−1.51964	−	25.0880i	−0.0623517	−	1.02937i
$595$	−0.525339	−	0.303304i	−0.0215368	−	0.0124343i
$596$	−1.69498	−	6.32574i	−0.0694290	−	0.259112i
$597$	−2.07068	−	1.66752i	−0.0847471	−	0.0682470i
$598$	17.6001	+	5.08817i	0.719721	+	0.208071i
$599$		−	40.3004i		−	1.64663i	−0.567586	−	0.823314i	$-0.692123\pi$
$599$		−	40.3004i		−	1.64663i	0.567586	−	0.823314i	$-0.307877\pi$
$600$	−2.53956	+	5.74585i	−0.103677	+	0.234573i
$601$	−6.18901	+	10.7197i	−0.252455	+	0.437265i	−0.964201	−	0.265172i	$-0.914571\pi$
$601$	−6.18901	+	10.7197i	−0.252455	+	0.437265i	0.711746	+	0.702437i	$0.247905\pi$
$602$	0.146580	+	0.253885i	0.00597417	+	0.0103476i
$603$	−29.1869	−	18.7298i	−1.18858	−	0.762737i
$604$	−21.4395	−	5.74469i	−0.872360	−	0.233748i
$605$	−14.0315	−	3.75973i	−0.570462	−	0.152855i
$606$	−6.26022	+	0.675152i	−0.254304	+	0.0274262i
$607$	−19.4537	−	33.6949i	−0.789603	−	1.36763i	−0.926210	−	0.377007i	$-0.876953\pi$
$607$	−19.4537	−	33.6949i	−0.789603	−	1.36763i	0.136607	−	0.990625i	$-0.456380\pi$
$608$	2.84839	−	4.93356i	0.115517	−	0.200082i
$609$	−3.36047	−	1.48527i	−0.136173	−	0.0601861i
$610$			13.8355i			0.560185i
$611$	−30.1982	−	31.4075i	−1.22169	−	1.27061i
$612$	1.51734	−	0.331135i	0.0613348	−	0.0133853i
$613$	11.8801	+	44.3370i	0.479831	+	1.79075i	0.602286	+	0.798280i	$0.294257\pi$
$613$	11.8801	+	44.3370i	0.479831	+	1.79075i	−0.122455	+	0.992474i	$0.539077\pi$
$614$	−1.29488	−	0.747599i	−0.0522571	−	0.0301706i
$615$	−2.08914	+	13.4259i	−0.0842422	+	0.541386i
$616$	−3.42031	+	3.42031i	−0.137808	+	0.137808i
$617$	−11.9499	+	44.5976i	−0.481084	+	1.79543i	0.115996	+	0.993250i	$0.462994\pi$
$617$	−11.9499	+	44.5976i	−0.481084	+	1.79543i	−0.597081	+	0.802181i	$0.703673\pi$
$618$	18.6864	−	13.6541i	0.751679	−	0.549249i
$619$	27.7189	+	27.7189i	1.11412	+	1.11412i	0.992588	+	0.121530i	$0.0387802\pi$
$619$	27.7189	+	27.7189i	1.11412	+	1.11412i	0.121530	+	0.992588i	$0.461220\pi$
$620$	5.89947	−	3.40606i	0.236928	−	0.136791i
$621$	−22.0258	+	14.5599i	−0.883863	+	0.584269i
$622$	−6.11184	+	1.63766i	−0.245062	+	0.0656643i
$623$	−2.77347			−0.111117
$624$	−1.08111	+	6.15071i	−0.0432792	+	0.246225i
$625$	−6.28943			−0.251577
$626$	−25.8413	+	6.92415i	−1.03283	+	0.276745i
$627$	−44.5110	+	17.2249i	−1.77760	+	0.687895i
$628$	−14.1196	+	8.15196i	−0.563434	+	0.325299i
$629$	3.73772	+	3.73772i	0.149033	+	0.149033i
$630$	−0.164928	+	3.51145i	−0.00657090	+	0.139900i
$631$	10.3812	−	38.7430i	0.413267	−	1.54233i	−0.375014	−	0.927019i	$-0.622362\pi$
$631$	10.3812	−	38.7430i	0.413267	−	1.54233i	0.788281	−	0.615315i	$-0.210971\pi$
$632$	1.79103	−	1.79103i	0.0712432	−	0.0712432i
$633$	−17.4305	−	2.71227i	−0.692800	−	0.107803i
$634$	16.6761	+	9.62793i	0.662291	+	0.382374i
$635$	1.34485	+	5.01906i	0.0533689	+	0.199175i
$636$	10.3500	−	12.8523i	0.410405	−	0.509628i
$637$	−1.86371	+	3.08652i	−0.0738428	+	0.122292i
$638$		−	10.2605i		−	0.406215i
$639$	2.59163	+	5.01885i	0.102523	+	0.198542i
$640$	0.585888	−	1.01479i	0.0231592	−	0.0401130i
$641$	24.9443	+	43.2048i	0.985241	+	1.70649i	0.640863	+	0.767656i	$0.278577\pi$
$641$	24.9443	+	43.2048i	0.985241	+	1.70649i	0.344378	+	0.938831i	$0.388090\pi$
$642$	0.278071	+	2.57837i	0.0109746	+	0.101760i
$643$	14.2810	+	3.82658i	0.563188	+	0.150906i	0.529171	−	0.848515i	$-0.322503\pi$
$643$	14.2810	+	3.82658i	0.563188	+	0.150906i	0.0340174	+	0.999421i	$0.489170\pi$
$644$	4.90814	+	1.31513i	0.193408	+	0.0518235i
$645$	0.0637986	+	0.591561i	0.00251207	+	0.0232927i
$646$	−1.47457	−	2.55402i	−0.0580160	−	0.100487i
$647$	9.53941	−	16.5227i	0.375033	−	0.649576i	−0.615299	−	0.788294i	$-0.710965\pi$
$647$	9.53941	−	16.5227i	0.375033	−	0.649576i	0.990332	+	0.138718i	$0.0442981\pi$
$648$	−5.73945	−	6.93244i	−0.225467	−	0.272332i
$649$		−	7.69926i		−	0.302222i
$650$	−12.6955	+	3.13606i	−0.497960	+	0.123006i
$651$	−6.31555	+	7.84247i	−0.247526	+	0.307371i
$652$	0.906537	+	3.38324i	0.0355027	+	0.132498i
$653$	3.37449	+	1.94826i	0.132054	+	0.0762415i	0.564572	−	0.825384i	$-0.309041\pi$
$653$	3.37449	+	1.94826i	0.132054	+	0.0762415i	−0.432518	+	0.901625i	$0.642375\pi$
$654$	22.6393	+	3.52278i	0.885265	+	0.137751i
$655$	11.8426	−	11.8426i	0.462728	−	0.462728i
$656$	−1.73273	+	6.46664i	−0.0676518	+	0.252480i
$657$	−19.8501	−	0.932331i	−0.774425	−	0.0363737i
$658$	−8.54481	−	8.54481i	−0.333111	−	0.333111i
$659$	3.30124	−	1.90597i	0.128598	−	0.0742462i	−0.434321	−	0.900758i	$-0.643012\pi$
$659$	3.30124	−	1.90597i	0.128598	−	0.0742462i	0.562919	+	0.826512i	$0.309678\pi$
$660$	−9.15551	+	3.54300i	−0.356378	+	0.137911i
$661$	−22.9665	+	6.15385i	−0.893292	+	0.239357i	−0.676133	−	0.736779i	$-0.736346\pi$
$661$	−22.9665	+	6.15385i	−0.893292	+	0.239357i	−0.217159	+	0.976136i	$0.569679\pi$
$662$	−9.35287			−0.363510
$663$	2.47769	+	2.07675i	0.0962256	+	0.0806544i
$664$	16.5766			0.643298
$665$	6.44789	−	1.72771i	0.250038	−	0.0669976i
$666$	9.30767	−	29.1839i	0.360665	−	1.13085i
$667$	−9.33449	+	5.38927i	−0.361433	+	0.208673i
$668$	10.6265	+	10.6265i	0.411151	+	0.411151i
$669$	2.74947	−	2.00902i	0.106301	−	0.0776734i
$670$	−3.50586	+	13.0840i	−0.135443	+	0.505480i
$671$	40.3847	−	40.3847i	1.55903	−	1.55903i
$672$	−0.266310	+	1.71146i	−0.0102732	+	0.0660208i
$673$	4.61841	+	2.66644i	0.178027	+	0.102784i	0.586365	−	0.810047i	$-0.300558\pi$
$673$	4.61841	+	2.66644i	0.178027	+	0.102784i	−0.408339	+	0.912831i	$0.633892\pi$
$674$	1.15886	+	4.32492i	0.0446375	+	0.166590i
$675$	8.41903	−	16.8611i	0.324049	−	0.648985i
$676$	−11.5047	+	6.05318i	−0.442490	+	0.232815i
$677$			17.4542i			0.670819i	0.942072	+	0.335410i	$0.108875\pi$
$677$			17.4542i			0.670819i	−0.942072	+	0.335410i	$0.891125\pi$
$678$	−27.1655	−	12.0067i	−1.04329	−	0.461114i
$679$	2.04586	−	3.54353i	0.0785127	−	0.135988i
$680$	−0.303304	−	0.525339i	−0.0116312	−	0.0201458i
$681$	8.80140	−	0.949212i	0.337270	−	0.0363739i
$682$	−27.1620	−	7.27804i	−1.04009	−	0.278690i
$683$	14.4342	+	3.86763i	0.552309	+	0.147991i	0.524170	−	0.851613i	$-0.324375\pi$
$683$	14.4342	+	3.86763i	0.552309	+	0.147991i	0.0281382	+	0.999604i	$0.491042\pi$
$684$	−9.23016	+	14.3835i	−0.352924	+	0.549965i
$685$	5.62597	+	9.74447i	0.214957	+	0.372317i
$686$	−0.500000	+	0.866025i	−0.0190901	+	0.0330650i
$687$	2.37688	−	5.37779i	0.0906838	−	0.205175i
$688$			0.293161i			0.0111766i
$689$	34.3444	+	0.674152i	1.30842	+	0.0256831i
$690$	8.03216	+	6.46831i	0.305779	+	0.246245i
$691$	−9.50395	−	35.4692i	−0.361547	−	1.34931i	−0.872042	−	0.489432i	$-0.837204\pi$
$691$	−9.50395	−	35.4692i	−0.361547	−	1.34931i	0.510494	−	0.859881i	$-0.329462\pi$
$692$	−3.70764	−	2.14061i	−0.140943	−	0.0813738i
$693$	10.7310	−	9.76821i	0.407638	−	0.371064i
$694$	−15.5534	+	15.5534i	−0.590398	+	0.590398i
$695$	4.73848	−	17.6842i	0.179741	−	0.670801i
$696$	−2.16762	−	2.96651i	−0.0821634	−	0.112445i
$697$	2.45067	+	2.45067i	0.0928256	+	0.0928256i
$698$	30.6176	−	17.6771i	1.15889	−	0.669086i
$699$	5.34394	+	13.8094i	0.202126	+	0.522318i
$700$	−3.50336	+	0.938722i	−0.132414	+	0.0354804i
$701$	−12.1730			−0.459768			−0.229884	−	0.973218i	$-0.573835\pi$
$701$	−12.1730			−0.459768			−0.229884	+	0.973218i	$0.573835\pi$
$702$	4.10549	−	18.2796i	0.154952	−	0.689920i
$703$	−58.1684			−2.19386
$704$	−4.67223	+	1.25192i	−0.176091	+	0.0471835i
$705$	−8.85133	−	22.8728i	−0.333360	−	0.861441i
$706$	2.63752	−	1.52277i	0.0992644	−	0.0573104i
$707$	−2.57055	−	2.57055i	−0.0966753	−	0.0966753i
$708$	−1.62654	−	2.22602i	−0.0611292	−	0.0836589i
$709$	−4.31325	+	16.0973i	−0.161987	+	0.604545i	0.836418	+	0.548092i	$0.184646\pi$
$709$	−4.31325	+	16.0973i	−0.161987	+	0.604545i	−0.998405	+	0.0564528i	$0.982021\pi$
$710$	1.56005	−	1.56005i	0.0585478	−	0.0585478i
$711$	−5.61925	+	5.11508i	−0.210738	+	0.191830i
$712$	−2.40190	−	1.38673i	−0.0900148	−	0.0519701i
$713$	7.64553	+	28.5335i	0.286327	+	1.06859i
$714$	0.698360	+	0.562390i	0.0261354	+	0.0210469i
$715$	−17.4942	−	10.5634i	−0.654244	−	0.395047i
$716$		−	10.6618i		−	0.398452i
$717$	19.8791	−	44.9772i	0.742398	−	1.67970i
$718$	6.15101	−	10.6539i	0.229554	−	0.397599i
$719$	3.40817	+	5.90313i	0.127103	+	0.220150i	0.922553	−	0.385870i	$-0.126099\pi$
$719$	3.40817	+	5.90313i	0.127103	+	0.220150i	−0.795450	+	0.606020i	$0.792765\pi$
$720$	−1.89856	+	2.95854i	−0.0707551	+	0.110258i
$721$	12.9066	+	3.45830i	0.480666	+	0.128794i
$722$	12.9949	+	3.48198i	0.483620	+	0.129586i
$723$	38.3021	−	4.13080i	1.42447	−	0.153626i
$724$	6.86168	+	11.8848i	0.255013	+	0.441695i
$725$	3.84678	−	6.66282i	0.142866	−	0.247451i
$726$	19.6395	+	8.68029i	0.728889	+	0.322156i
$727$		−	31.4461i		−	1.16627i	−0.812375	−	0.583135i	$-0.801826\pi$
$727$		−	31.4461i		−	1.16627i	0.812375	−	0.583135i	$-0.198174\pi$
$728$	−3.15728	+	1.74115i	−0.117017	+	0.0645312i
$729$	16.2236	+	21.5823i	0.600875	+	0.799343i
$730$	2.00891	+	7.49734i	0.0743530	+	0.277489i
$731$	0.131432	+	0.0758822i	0.00486118	+	0.00280661i
$732$	3.14442	−	20.2077i	0.116221	−	0.746899i
$733$	−3.85594	+	3.85594i	−0.142422	+	0.142422i	−0.774723	−	0.632301i	$-0.782111\pi$
$733$	−3.85594	+	3.85594i	−0.142422	+	0.142422i	0.632301	+	0.774723i	$0.282111\pi$
$734$	4.06624	−	15.1754i	0.150088	−	0.560135i
$735$	−1.63872	+	1.19740i	−0.0604450	+	0.0441669i
$736$	3.59301	+	3.59301i	0.132440	+	0.132440i
$737$	48.4244	−	27.9578i	1.78374	−	1.02984i
$738$	6.10265	−	19.1347i	0.224642	−	0.704357i
$739$	4.86945	−	1.30477i	0.179126	−	0.0479966i	−0.168141	−	0.985763i	$-0.553776\pi$
$739$	4.86945	−	1.30477i	0.179126	−	0.0479966i	0.347267	+	0.937766i	$0.387110\pi$
$740$	−11.9647			−0.439831
$741$	−35.4393	+	3.11981i	−1.30190	+	0.114609i
$742$	9.52725			0.349756
$743$	−17.4562	+	4.67738i	−0.640407	+	0.171597i	−0.564388	−	0.825510i	$-0.690888\pi$
$743$	−17.4562	+	4.67738i	−0.640407	+	0.171597i	−0.0760193	+	0.997106i	$0.524221\pi$
$744$	−9.39066	+	3.63400i	−0.344278	+	0.133229i
$745$	6.64573	−	3.83691i	0.243481	−	0.140574i
$746$	−1.49380	−	1.49380i	−0.0546918	−	0.0546918i
$747$	−49.6752	−	2.33318i	−1.81752	−	0.0853664i
$748$	−0.648098	+	2.41873i	−0.0236968	+	0.0884377i
$749$	−1.05872	+	1.05872i	−0.0386847	+	0.0386847i
$750$	−17.3008	−	2.69209i	−0.631737	−	0.0983012i
$751$	−39.0894	−	22.5683i	−1.42639	−	0.823528i	−0.429559	−	0.903039i	$-0.641331\pi$
$751$	−39.0894	−	22.5683i	−1.42639	−	0.823528i	−0.996834	+	0.0795108i	$0.974664\pi$
$752$	−3.12762	−	11.6724i	−0.114053	−	0.425650i
$753$	−17.7172	+	22.0007i	−0.645650	+	0.801749i
$754$	2.12410	−	7.34731i	0.0773551	−	0.267573i
$755$		−	26.0085i		−	0.946545i
$756$	1.03894	−	5.09123i	0.0377859	−	0.185166i
$757$	−21.5477	+	37.3217i	−0.783164	+	1.35648i	0.146925	+	0.989148i	$0.453062\pi$
$757$	−21.5477	+	37.3217i	−0.783164	+	1.35648i	−0.930090	+	0.367333i	$0.880271\pi$
$758$	−17.1930	−	29.7792i	−0.624478	−	1.08163i
$759$	−4.56472	−	42.3256i	−0.165689	−	1.53632i
$760$	6.44789	+	1.72771i	0.233890	+	0.0626705i
$761$	−36.4729	−	9.77289i	−1.32214	−	0.354267i	−0.472363	−	0.881404i	$-0.656599\pi$
$761$	−36.4729	−	9.77289i	−1.32214	−	0.354267i	−0.849780	+	0.527137i	$0.823265\pi$
$762$	−0.823560	−	7.63631i	−0.0298344	−	0.276634i
$763$	6.61404	+	11.4559i	0.239444	+	0.414730i
$764$	−9.09873	+	15.7595i	−0.329181	+	0.570157i
$765$	0.834969	+	1.61697i	0.0301884	+	0.0584617i
$766$		−	27.8236i		−	1.00531i
$767$	1.59389	−	5.51329i	0.0575519	−	0.199073i
$768$	−1.08636	+	1.34901i	−0.0392006	+	0.0486781i
$769$	−7.35795	−	27.4602i	−0.265335	−	0.990242i	−0.962045	−	0.272890i	$-0.912021\pi$
$769$	−7.35795	−	27.4602i	−0.265335	−	0.990242i	0.696711	−	0.717352i	$-0.254646\pi$
$770$	−4.90857	−	2.83396i	−0.176893	−	0.102129i
$771$	−5.12691	−	0.797771i	−0.184641	−	0.0287310i
$772$	−0.610626	+	0.610626i	−0.0219769	+	0.0219769i
$773$	2.26818	−	8.46496i	0.0815808	−	0.304464i	−0.913064	−	0.407816i	$-0.866290\pi$
$773$	2.26818	−	8.46496i	0.0815808	−	0.304464i	0.994645	+	0.103353i	$0.0329571\pi$
$774$	0.0412626	−	0.878513i	0.00148315	−	0.0315775i
$775$	−14.9095	−	14.9095i	−0.535566	−	0.535566i
$776$	3.54353	−	2.04586i	0.127205	−	0.0734419i
$777$	16.4936	−	6.38269i	0.591705	−	0.228978i
$778$	15.4683	−	4.14471i	0.554564	−	0.148595i
$779$	−38.1386			−1.36646
$780$	−7.28954	+	0.641715i	−0.261007	+	0.0229771i
$781$	−9.10732			−0.325885
$782$	2.54087	−	0.680823i	0.0908612	−	0.0243462i
$783$	6.07816	+	9.19484i	0.217216	+	0.328597i
$784$	−0.866025	+	0.500000i	−0.0309295	+	0.0178571i
$785$	−13.5089	−	13.5089i	−0.482155	−	0.482155i
$786$	−19.9884	+	14.6054i	−0.712961	+	0.520957i
$787$	−5.18723	+	19.3590i	−0.184905	+	0.690074i	0.809746	+	0.586781i	$0.199605\pi$
$787$	−5.18723	+	19.3590i	−0.184905	+	0.690074i	−0.994651	+	0.103294i	$0.967062\pi$
$788$	−14.9600	+	14.9600i	−0.532926	+	0.532926i
$789$	−1.08396	+	6.96611i	−0.0385900	+	0.248000i
$790$	2.57035	+	1.48399i	0.0914489	+	0.0527980i
$791$	−4.43814	−	16.5634i	−0.157802	−	0.588925i
$792$	14.1774	−	3.09400i	0.503774	−	0.109941i
$793$	37.2791	−	20.5583i	1.32382	−	0.730048i
$794$			13.9657i			0.495623i
$795$	17.6858	+	7.81681i	0.627251	+	0.277234i
$796$	0.767481	−	1.32932i	0.0272026	−	0.0471163i
$797$	−5.16123	−	8.93952i	−0.182820	−	0.316654i	0.760020	−	0.649900i	$-0.225189\pi$
$797$	−5.16123	−	8.93952i	−0.182820	−	0.316654i	−0.942840	+	0.333246i	$0.891856\pi$
$798$	−9.81023	+	1.05801i	−0.347278	+	0.0374532i
$799$	−6.04263	−	1.61912i	−0.213773	−	0.0572802i
$800$	−3.50336	−	0.938722i	−0.123862	−	0.0331888i
$801$	7.00257	+	4.49369i	0.247424	+	0.158777i
$802$	−12.9407	−	22.4139i	−0.456951	−	0.791463i
$803$	16.0202	−	27.7479i	0.565342	−	0.979202i
$804$	8.09416	−	18.3133i	0.285459	−	0.645861i
$805$			5.95412i			0.209855i
$806$	−17.9435	−	10.8347i	−0.632032	−	0.381635i
$807$	−4.18218	−	3.36792i	−0.147220	−	0.118556i
$808$	−0.940885	−	3.51143i	−0.0331002	−	0.123532i
$809$	−42.5731	−	24.5796i	−1.49679	−	0.864172i	−0.496796	−	0.867867i	$-0.665490\pi$
$809$	−42.5731	−	24.5796i	−1.49679	−	0.864172i	−0.999993	+	0.00369576i	$0.998824\pi$
$810$	6.10582	−	8.59864i	0.214537	−	0.302125i
$811$	9.89969	−	9.89969i	0.347625	−	0.347625i	−0.511599	−	0.859224i	$-0.670947\pi$
$811$	9.89969	−	9.89969i	0.347625	−	0.347625i	0.859224	+	0.511599i	$0.170947\pi$
$812$	0.549013	−	2.04895i	0.0192666	−	0.0719039i
$813$	−15.6788	−	21.4573i	−0.549879	−	0.752541i
$814$	34.9239	+	34.9239i	1.22408	+	1.22408i
$815$	−3.55438	+	2.05212i	−0.124505	+	0.0718828i
$816$	0.323602	+	0.836224i	0.0113283	+	0.0292737i
$817$	−1.61317	+	0.432246i	−0.0564375	+	0.0151224i
$818$	7.54280			0.263728
$819$	9.70647	−	4.77330i	0.339172	−	0.166793i
$820$	−7.84475			−0.273951
$821$	16.1341	−	4.32313i	0.563085	−	0.150878i	0.0339617	−	0.999423i	$-0.489188\pi$
$821$	16.1341	−	4.32313i	0.563085	−	0.150878i	0.529123	+	0.848545i	$0.322521\pi$
$822$	−6.00247	−	15.5111i	−0.209360	−	0.541011i
$823$	4.33765	−	2.50434i	0.151201	−	0.0872959i	−0.422491	−	0.906367i	$-0.638844\pi$
$823$	4.33765	−	2.50434i	0.151201	−	0.0872959i	0.573692	+	0.819071i	$0.305511\pi$
$824$	9.44826	+	9.44826i	0.329146	+	0.329146i
$825$	17.9274	+	24.5347i	0.624152	+	0.854188i
$826$	0.411970	−	1.53749i	0.0143343	−	0.0534962i
$827$	−20.9459	+	20.9459i	−0.728359	+	0.728359i	−0.970293	−	0.241934i	$-0.922218\pi$
$827$	−20.9459	+	20.9459i	−0.728359	+	0.728359i	0.241934	+	0.970293i	$0.422218\pi$
$828$	−10.2614	−	11.2729i	−0.356610	−	0.391760i
$829$	31.5815	+	18.2336i	1.09687	+	0.633280i	0.935398	−	0.353597i	$-0.115042\pi$
$829$	31.5815	+	18.2336i	1.09687	+	0.633280i	0.161475	+	0.986877i	$0.448375\pi$
$830$	5.02733	+	18.7622i	0.174501	+	0.651247i
$831$	1.63991	+	1.32063i	0.0568880	+	0.0458120i
$832$	−3.60486	−	0.0707604i	−0.124976	−	0.00245317i
$833$			0.517684i			0.0179367i
$834$	−10.9400	+	24.7521i	−0.378820	+	0.857095i
$835$	−8.80478	+	15.2503i	−0.304702	+	0.527759i
$836$	−13.7778	−	23.8638i	−0.476515	−	0.825348i
$837$	28.6525	−	9.56825i	0.990374	−	0.330727i
$838$	−16.0547	−	4.30185i	−0.554601	−	0.148605i
$839$	49.7434	+	13.3287i	1.71733	+	0.460158i	0.977203	−	0.212306i	$-0.0680973\pi$
$839$	49.7434	+	13.3287i	1.71733	+	0.460158i	0.740130	+	0.672464i	$0.234764\pi$
$840$	−2.01787	+	0.217623i	−0.0696232	+	0.00750872i
$841$	−12.2502	−	21.2180i	−0.422421	−	0.731654i
$842$	−6.22805	+	10.7873i	−0.214633	+	0.371755i
$843$	4.06792	+	1.79795i	0.140107	+	0.0619246i
$844$		−	10.1846i		−	0.350568i
$845$	−10.3404	−	11.1858i	−0.355721	−	0.384804i
$846$	7.72962	+	35.4189i	0.265750	+	1.21773i
$847$	3.20858	+	11.9746i	0.110248	+	0.411451i
$848$	8.25084	+	4.76362i	0.283335	+	0.163584i
$849$	−2.55344	+	16.4098i	−0.0876339	+	0.563183i
$850$	−1.32767	+	1.32767i	−0.0455387	+	0.0455387i
$851$	13.4285	−	50.1158i	0.460322	−	1.71795i
$852$	−2.63312	+	1.92401i	−0.0902091	+	0.0659154i
$853$	−14.1855	−	14.1855i	−0.485702	−	0.485702i	0.421245	−	0.906947i	$-0.361593\pi$
$853$	−14.1855	−	14.1855i	−0.485702	−	0.485702i	−0.906947	+	0.421245i	$0.861593\pi$
$854$	10.2255	−	5.90367i	0.349908	−	0.202019i
$855$	−19.0792	−	6.08496i	−0.652495	−	0.208101i
$856$	−1.44624	+	0.387518i	−0.0494313	+	0.0132451i
$857$	10.4375			0.356538			0.178269	−	0.983982i	$-0.442950\pi$
$857$	10.4375			0.356538			0.178269	+	0.983982i	$0.442950\pi$
$858$	23.1506	+	19.4044i	0.790349	+	0.662456i
$859$	−34.6814			−1.18331			−0.591656	−	0.806190i	$-0.701526\pi$
$859$	−34.6814			−1.18331			−0.591656	+	0.806190i	$0.701526\pi$
$860$	−0.331813	+	0.0889091i	−0.0113147	+	0.00303177i
$861$	10.8142	−	4.18486i	0.368546	−	0.142620i
$862$	−16.5218	+	9.53886i	−0.562734	+	0.324895i
$863$	31.2962	+	31.2962i	1.06533	+	1.06533i	0.997711	+	0.0676228i	$0.0215415\pi$
$863$	31.2962	+	31.2962i	1.06533	+	1.06533i	0.0676228	+	0.997711i	$0.478459\pi$
$864$	3.44536	−	3.88966i	0.117214	−	0.132329i
$865$	1.29840	−	4.84569i	0.0441469	−	0.164758i
$866$	−14.2286	+	14.2286i	−0.483507	+	0.483507i
$867$	−28.6361	−	4.45591i	−0.972532	−	0.151331i
$868$	−5.03464	−	2.90675i	−0.170887	−	0.0986616i
$869$	−3.17098	−	11.8343i	−0.107568	−	0.401450i
$870$	2.70025	−	3.35309i	0.0915471	−	0.113680i
$871$	40.4635	−	9.99533i	1.37105	−	0.338679i
$872$			13.2281i			0.447959i
$873$	−10.9068	+	5.63205i	−0.369140	+	0.190616i
$874$	−14.4735	+	25.0688i	−0.489573	+	0.847965i
$875$	−5.05442	−	8.75451i	−0.170871	−	0.295956i
$876$	−1.23021	−	11.4069i	−0.0415650	−	0.385404i
$877$	−10.6929	−	2.86516i	−0.361075	−	0.0967497i	0.0737208	−	0.997279i	$-0.476513\pi$
$877$	−10.6929	−	2.86516i	−0.361075	−	0.0967497i	−0.434795	+	0.900529i	$0.643179\pi$
$878$	24.8239	+	6.65155i	0.837766	+	0.224479i
$879$	3.91440	+	36.2956i	0.132030	+	1.22422i
$880$	−2.83396	−	4.90857i	−0.0955329	−	0.165468i
$881$	−14.9885	+	25.9608i	−0.504974	+	0.874641i	0.495009	+	0.868888i	$0.335165\pi$
$881$	−14.9885	+	25.9608i	−0.504974	+	0.874641i	−0.999983	+	0.00575302i	$0.998169\pi$
$882$	2.66559	−	1.37645i	0.0897551	−	0.0463476i
$883$		−	23.3378i		−	0.785381i	−0.919671	−	0.392690i	$-0.871544\pi$
$883$		−	23.3378i		−	0.785381i	0.919671	−	0.392690i	$-0.128456\pi$
$884$	−0.964811	+	1.59784i	−0.0324501	+	0.0537412i
$885$	2.02622	−	2.51610i	0.0681107	−	0.0845778i
$886$	0.00922912	+	0.0344435i	0.000310058	+	0.00115715i
$887$	−14.8835	−	8.59297i	−0.499738	−	0.288524i	0.228868	−	0.973458i	$-0.426498\pi$
$887$	−14.8835	−	8.59297i	−0.499738	−	0.288524i	−0.728605	+	0.684934i	$0.759831\pi$
$888$	17.4752	+	2.71923i	0.586430	+	0.0912513i
$889$	3.13559	−	3.13559i	0.105164	−	0.105164i
$890$	0.841132	−	3.13915i	0.0281948	−	0.105224i
$891$	−42.9210	+	7.27630i	−1.43791	+	0.243765i
$892$	1.39019	+	1.39019i	0.0465470	+	0.0465470i
$893$	59.6180	−	34.4205i	1.99504	−	1.15184i
$894$	−10.5785	+	4.09368i	−0.353799	+	0.136913i
$895$	12.0676	−	3.23350i	0.403375	−	0.108084i
$896$	−1.00000			−0.0334077
$897$	5.49345	−	31.2535i	0.183421	−	1.04352i
$898$	27.0334			0.902117
$899$	11.9116	−	3.19169i	0.397273	−	0.106449i
$900$	10.3664	+	3.30617i	0.345546	+	0.110206i
$901$	4.27132	−	2.46605i	0.142298	−	0.0821560i
$902$	22.8981	+	22.8981i	0.762424	+	0.762424i
$903$	0.409983	−	0.299573i	0.0136434	−	0.00996915i
$904$	4.43814	−	16.5634i	0.147610	−	0.550889i
$905$	−11.3708	+	11.3708i	−0.377977	+	0.377977i
$906$	−5.91097	+	37.9871i	−0.196379	+	1.26204i
$907$	20.9403	+	12.0899i	0.695311	+	0.401438i	0.805598	−	0.592462i	$-0.201844\pi$
$907$	20.9403	+	12.0899i	0.695311	+	0.401438i	−0.110288	+	0.993900i	$0.535177\pi$
$908$	1.32281	+	4.93680i	0.0438991	+	0.163834i
$909$	2.32531	+	10.6551i	0.0771257	+	0.353408i
$910$	−2.92825	−	3.04551i	−0.0970704	−	0.100958i
$911$		−	20.0949i		−	0.665774i	−0.942967	−	0.332887i	$-0.891977\pi$
$911$		−	20.0949i		−	0.665774i	0.942967	−	0.332887i	$-0.108023\pi$
$912$	−9.02491	−	3.98885i	−0.298845	−	0.132084i
$913$	40.0910	−	69.4396i	1.32682	−	2.29812i
$914$	−15.5448	−	26.9245i	−0.514178	−	0.890582i
$915$	23.8257	−	2.56955i	0.787654	−	0.0849468i
$916$	3.27894	+	0.878590i	0.108339	+	0.0290294i
$917$	−13.8058	−	3.69925i	−0.455907	−	0.122160i
$918$	−0.852038	−	2.55146i	−0.0281214	−	0.0842106i
$919$	−13.4305	−	23.2624i	−0.443032	−	0.767354i	0.554881	−	0.831930i	$-0.312764\pi$
$919$	−13.4305	−	23.2624i	−0.443032	−	0.767354i	−0.997913	+	0.0645756i	$0.979431\pi$
$920$	−2.97706	+	5.15642i	−0.0981508	+	0.170002i
$921$	−1.04693	+	2.36871i	−0.0344974	+	0.0780517i
$922$		−	18.8979i		−	0.622371i
$923$	−6.52157	−	1.88538i	−0.214660	−	0.0620580i
$924$	6.52521	+	5.25477i	0.214664	+	0.172869i
$925$	9.58505	+	35.7719i	0.315154	+	1.17617i
$926$	1.17488	+	0.678320i	0.0386091	+	0.0222910i
$927$	−26.9837	−	29.6434i	−0.886262	−	0.973618i
$928$	1.49993	−	1.49993i	0.0492377	−	0.0492377i
$929$	−4.56360	+	17.0316i	−0.149727	+	0.558789i	0.849772	+	0.527150i	$0.176739\pi$
$929$	−4.56360	+	17.0316i	−0.149727	+	0.558789i	−0.999499	+	0.0316389i	$0.989927\pi$
$930$	−6.96111	−	9.52669i	−0.228264	−	0.312393i
$931$	−4.02823	−	4.02823i	−0.132020	−	0.132020i
$932$	−7.40365	+	4.27450i	−0.242515	+	0.140016i
$933$	3.95526	+	10.2208i	0.129489	+	0.334615i
$934$	−27.3544	+	7.32959i	−0.895064	+	0.239832i
$935$	−2.93419			−0.0959584
$936$	10.7927	+	0.719434i	0.352770	+	0.0235154i
$937$	53.8449			1.75904			0.879519	−	0.475864i	$-0.157865\pi$
$937$	53.8449			1.75904			0.879519	+	0.475864i	$0.157865\pi$
$938$	11.1660	−	2.99192i	0.364583	−	0.0976896i
$939$	16.7231	+	43.2144i	0.545738	+	1.41025i
$940$	12.2629	−	7.07998i	0.399971	−	0.230923i
$941$	−5.19843	−	5.19843i	−0.169464	−	0.169464i	0.617280	−	0.786744i	$-0.288235\pi$
$941$	−5.19843	−	5.19843i	−0.169464	−	0.169464i	−0.786744	+	0.617280i	$0.788235\pi$
$942$	16.6605	+	22.8009i	0.542829	+	0.742894i
$943$	8.80449	−	32.8588i	0.286714	−	1.07003i
$944$	1.12552	−	1.12552i	0.0366326	−	0.0366326i
$945$	6.07758	−	0.368134i	0.197704	−	0.0119754i
$946$	1.22805	+	0.709015i	0.0399274	+	0.0230521i
$947$	−9.58848	−	35.7847i	−0.311584	−	1.16285i	−0.927128	−	0.374744i	$-0.877731\pi$
$947$	−9.58848	−	35.7847i	−0.311584	−	1.16285i	0.615544	−	0.788102i	$-0.288936\pi$
$948$	−3.41690	−	2.75163i	−0.110976	−	0.0893689i
$949$	17.2161	−	16.5532i	0.558858	−	0.537340i
$950$		−	20.6619i		−	0.670361i
$951$	13.4828	−	30.5054i	0.437210	−	0.989204i
$952$	−0.258842	+	0.448327i	−0.00838911	+	0.0145304i
$953$	−5.85318	−	10.1380i	−0.189603	−	0.328402i	0.755515	−	0.655131i	$-0.227387\pi$
$953$	−5.85318	−	10.1380i	−0.189603	−	0.328402i	−0.945118	+	0.326729i	$0.894053\pi$
$954$	−24.0548	−	15.4364i	−0.778802	−	0.499773i
$955$	−20.5968	−	5.51889i	−0.666496	−	0.178587i
$956$	27.4235	+	7.34810i	0.886938	+	0.237654i
$957$	−17.6692	+	1.90558i	−0.571163	+	0.0615987i
$958$	10.6032	+	18.3653i	0.342574	+	0.593356i
$959$	4.80124	−	8.31599i	0.155040	−	0.268537i
$960$	−1.85634	−	0.820469i	−0.0599131	−	0.0264805i
$961$		−	2.79684i		−	0.0902207i
$962$	17.7784	+	32.2381i	0.573199	+	1.03940i
$963$	4.38847	−	0.957714i	0.141417	−	0.0308619i
$964$	5.75665	+	21.4841i	0.185409	+	0.691956i
$965$	−0.876325	−	0.505946i	−0.0282099	−	0.0162870i
$966$	1.35320	−	8.69639i	0.0435385	−	0.279802i
$967$	−25.0831	+	25.0831i	−0.806617	+	0.806617i	−0.984120	−	0.177503i	$-0.943198\pi$
$967$	−25.0831	+	25.0831i	−0.806617	+	0.806617i	0.177503	+	0.984120i	$0.443198\pi$
$968$	−3.20858	+	11.9746i	−0.103128	+	0.384877i
$969$	−4.12433	+	3.01363i	−0.132493	+	0.0968118i
$970$	3.39027	+	3.39027i	0.108855	+	0.108855i
$971$	16.3331	−	9.42992i	0.524154	−	0.302621i	−0.214478	−	0.976729i	$-0.568805\pi$
$971$	16.3331	−	9.42992i	0.524154	−	0.302621i	0.738633	+	0.674108i	$0.235472\pi$
$972$	−10.8722	+	11.1712i	−0.348725	+	0.358316i
$973$	−15.0918	+	4.04385i	−0.483822	+	0.129640i
$974$	26.1828			0.838950
$975$	7.75832	+	21.2801i	0.248465	+	0.681508i
$976$	11.8073			0.377944
$977$	41.4004	−	11.0932i	1.32452	−	0.354903i	0.473849	−	0.880606i	$-0.342864\pi$
$977$	41.4004	−	11.0932i	1.32452	−	0.354903i	0.850668	+	0.525703i	$0.176198\pi$
$978$	5.65780	−	2.18946i	0.180917	−	0.0700111i
$979$	−11.6181	+	6.70770i	−0.371315	+	0.214379i
$980$	−0.828570	−	0.828570i	−0.0264677	−	0.0264677i
$981$	1.86186	−	39.6405i	0.0594447	−	1.26562i
$982$	−2.74587	+	10.2477i	−0.0876244	+	0.327019i
$983$	−20.7752	+	20.7752i	−0.662625	+	0.662625i	−0.955998	−	0.293373i	$-0.905222\pi$
$983$	−20.7752	+	20.7752i	−0.662625	+	0.662625i	0.293373	+	0.955998i	$0.405222\pi$
$984$	11.4578	+	1.78288i	0.365261	+	0.0568363i
$985$	−21.4694	−	12.3954i	−0.684073	−	0.394949i
$986$	−0.284215	−	1.06071i	−0.00905126	−	0.0337797i
$987$	−13.1278	+	16.3017i	−0.417862	+	0.518888i
$988$	−4.92576	−	19.9407i	−0.156709	−	0.634397i
$989$		−	1.48963i		−	0.0473675i
$990$	7.80164	+	15.1084i	0.247953	+	0.480176i
$991$	−3.23933	+	5.61068i	−0.102901	+	0.178229i	−0.912879	−	0.408231i	$-0.866146\pi$
$991$	−3.23933	+	5.61068i	−0.102901	+	0.178229i	0.809978	+	0.586460i	$0.199479\pi$
$992$	−2.90675	−	5.03464i	−0.0922895	−	0.159850i
$993$	1.73703	+	16.1063i	0.0551228	+	0.511117i
$994$	−1.81867	−	0.487312i	−0.0576848	−	0.0154566i
$995$	1.73734	+	0.465519i	0.0550775	+	0.0147580i
$996$	−3.07863	−	28.5461i	−0.0975501	−	0.904516i
$997$	21.9402	+	38.0016i	0.694854	+	1.20352i	0.970230	+	0.242185i	$0.0778642\pi$
$997$	21.9402	+	38.0016i	0.694854	+	1.20352i	−0.275376	+	0.961337i	$0.588802\pi$
$998$	−16.7930	+	29.0863i	−0.531572	+	0.920709i
$999$	−51.9852	−	10.6084i	−1.64474	−	0.335633i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bu.b.71.10	yes	56
3.2	odd	2		546.2.bu.a.71.7	✓	56
13.11	odd	12		546.2.bu.a.323.7	yes	56
39.11	even	12	inner	546.2.bu.b.323.10	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bu.a.71.7	✓	56	3.2	odd	2
546.2.bu.a.323.7	yes	56	13.11	odd	12
546.2.bu.b.71.10	yes	56	1.1	even	1	trivial
546.2.bu.b.323.10	yes	56	39.11	even	12	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bu (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 - 0.258819i) q^{2} +(-0.625096 - 1.61532i) q^{3} +(0.866025 - 0.500000i) q^{4} +(0.828570 + 0.828570i) q^{5} +(-1.02187 - 1.39849i) q^{6} +(0.258819 - 0.965926i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.21851 + 2.01946i) q^{9} +O(q^{10})\)	\(q+(0.965926 - 0.258819i) q^{2} +(-0.625096 - 1.61532i) q^{3} +(0.866025 - 0.500000i) q^{4} +(0.828570 + 0.828570i) q^{5} +(-1.02187 - 1.39849i) q^{6} +(0.258819 - 0.965926i) q^{7} +(0.707107 - 0.707107i) q^{8} +(-2.21851 + 2.01946i) q^{9} +(1.01479 + 0.585888i) q^{10} +(-1.25192 - 4.67223i) q^{11} +(-1.34901 - 1.08636i) q^{12} +(0.0707604 - 3.60486i) q^{13} -1.00000i q^{14} +(0.820469 - 1.85634i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-0.258842 - 0.448327i) q^{17} +(-1.62024 + 2.52484i) q^{18} +(5.50267 + 1.47444i) q^{19} +(1.13185 + 0.303278i) q^{20} +(-1.72206 + 0.185721i) q^{21} +(-2.41852 - 4.18900i) q^{22} +(-2.54064 + 4.40052i) q^{23} +(-1.58421 - 0.700193i) q^{24} -3.62694i q^{25} +(-0.864656 - 3.50034i) q^{26} +(4.64885 + 2.32125i) q^{27} +(-0.258819 - 0.965926i) q^{28} +(1.83703 + 1.06061i) q^{29} +(0.312056 - 2.00544i) q^{30} +(4.11077 - 4.11077i) q^{31} +(0.258819 - 0.965926i) q^{32} +(-6.76456 + 4.94284i) q^{33} +(-0.366058 - 0.366058i) q^{34} +(1.01479 - 0.585888i) q^{35} +(-0.911557 + 2.85816i) q^{36} +(-9.86282 + 2.64273i) q^{37} +5.69678 q^{38} +(-5.86723 + 2.13908i) q^{39} +1.17178 q^{40} +(-6.46664 + 1.73273i) q^{41} +(-1.61532 + 0.625096i) q^{42} +(-0.253885 + 0.146580i) q^{43} +(-3.42031 - 3.42031i) q^{44} +(-3.51145 - 0.164928i) q^{45} +(-1.31513 + 4.90814i) q^{46} +(8.54481 - 8.54481i) q^{47} +(-1.71146 - 0.266310i) q^{48} +(-0.866025 - 0.500000i) q^{49} +(-0.938722 - 3.50336i) q^{50} +(-0.562390 + 0.698360i) q^{51} +(-1.74115 - 3.15728i) q^{52} +9.52725i q^{53} +(5.09123 + 1.03894i) q^{54} +(2.83396 - 4.90857i) q^{55} +(-0.500000 - 0.866025i) q^{56} +(-1.05801 - 9.81023i) q^{57} +(2.04895 + 0.549013i) q^{58} +(1.53749 + 0.411970i) q^{59} +(-0.217623 - 2.01787i) q^{60} +(5.90367 + 10.2255i) q^{61} +(2.90675 - 5.03464i) q^{62} +(1.37645 + 2.66559i) q^{63} -1.00000i q^{64} +(3.04551 - 2.92825i) q^{65} +(-5.25477 + 6.52521i) q^{66} +(2.99192 + 11.1660i) q^{67} +(-0.448327 - 0.258842i) q^{68} +(8.69639 + 1.35320i) q^{69} +(0.828570 - 0.828570i) q^{70} +(0.487312 - 1.81867i) q^{71} +(-0.140751 + 2.99670i) q^{72} +(4.68386 + 4.68386i) q^{73} +(-8.84276 + 5.10537i) q^{74} +(-5.85867 + 2.26719i) q^{75} +(5.50267 - 1.47444i) q^{76} -4.83704 q^{77} +(-5.11367 + 3.58474i) q^{78} +2.53289 q^{79} +(1.13185 - 0.303278i) q^{80} +(0.843575 - 8.96038i) q^{81} +(-5.79783 + 3.34738i) q^{82} +(11.7215 + 11.7215i) q^{83} +(-1.39849 + 1.02187i) q^{84} +(0.157002 - 0.585939i) q^{85} +(-0.207296 + 0.207296i) q^{86} +(0.564904 - 3.63038i) q^{87} +(-4.18900 - 2.41852i) q^{88} +(-0.717827 - 2.67897i) q^{89} +(-3.43449 + 0.749523i) q^{90} +(-3.46371 - 1.00135i) q^{91} +5.08128i q^{92} +(-9.20983 - 4.07058i) q^{93} +(6.04209 - 10.4652i) q^{94} +(3.33767 + 5.78102i) q^{95} +(-1.72206 + 0.185721i) q^{96} +(3.95229 + 1.05901i) q^{97} +(-0.965926 - 0.258819i) q^{98} +(12.2128 + 7.83718i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 8 q^{6} - 24 q^{9}+O(q^{10}) \) 56 * q + 8 * q^6 - 24 * q^9	\( 56 q + 8 q^{6} - 24 q^{9} + 24 q^{10} + 8 q^{11} + 24 q^{13} + 4 q^{15} + 28 q^{16} - 4 q^{17} - 8 q^{18} + 8 q^{19} + 4 q^{21} - 8 q^{23} - 8 q^{24} - 4 q^{26} - 24 q^{27} - 8 q^{30} - 8 q^{31} + 8 q^{33} - 24 q^{34} + 24 q^{35} - 12 q^{36} - 8 q^{37} - 20 q^{39} - 28 q^{41} + 8 q^{44} + 72 q^{45} - 20 q^{46} + 64 q^{50} + 16 q^{54} + 8 q^{55} - 28 q^{56} + 4 q^{58} - 8 q^{59} + 20 q^{60} + 8 q^{61} - 32 q^{62} - 16 q^{63} - 24 q^{65} + 32 q^{66} - 16 q^{69} - 112 q^{71} + 8 q^{73} + 48 q^{74} + 40 q^{75} + 8 q^{76} + 16 q^{79} + 12 q^{81} - 4 q^{83} - 4 q^{84} + 32 q^{85} - 16 q^{86} - 144 q^{87} + 88 q^{89} - 8 q^{90} - 8 q^{91} + 52 q^{93} - 8 q^{94} - 48 q^{95} + 4 q^{96} - 64 q^{97} + 56 q^{99}+O(q^{100}) \) 56 * q + 8 * q^6 - 24 * q^9 + 24 * q^10 + 8 * q^11 + 24 * q^13 + 4 * q^15 + 28 * q^16 - 4 * q^17 - 8 * q^18 + 8 * q^19 + 4 * q^21 - 8 * q^23 - 8 * q^24 - 4 * q^26 - 24 * q^27 - 8 * q^30 - 8 * q^31 + 8 * q^33 - 24 * q^34 + 24 * q^35 - 12 * q^36 - 8 * q^37 - 20 * q^39 - 28 * q^41 + 8 * q^44 + 72 * q^45 - 20 * q^46 + 64 * q^50 + 16 * q^54 + 8 * q^55 - 28 * q^56 + 4 * q^58 - 8 * q^59 + 20 * q^60 + 8 * q^61 - 32 * q^62 - 16 * q^63 - 24 * q^65 + 32 * q^66 - 16 * q^69 - 112 * q^71 + 8 * q^73 + 48 * q^74 + 40 * q^75 + 8 * q^76 + 16 * q^79 + 12 * q^81 - 4 * q^83 - 4 * q^84 + 32 * q^85 - 16 * q^86 - 144 * q^87 + 88 * q^89 - 8 * q^90 - 8 * q^91 + 52 * q^93 - 8 * q^94 - 48 * q^95 + 4 * q^96 - 64 * q^97 + 56 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more